Savage Road SignsCross-road optimization - what is the proper way to solve this type of puzzle?Ernie and the CalendarErnie and the Alien InvasionDroning On in CirclesBuilding a cheap roadErnie and the Grand TourErnie and the slice of PiErnie and the Disco Unicorn4x4 Sliding Puzzle with a twistFinding unique number properties

Savage Road Signs

How to befriend someone who doesn't like to talk?

DateTime.addMonths skips a month (from feb to mar)

Was planting UN flag on Moon ever discussed?

Why does there seem to be an extreme lack of public trashcans in Taiwan?

That's not my X, its Y is too Z

How do I type a hyphen in iOS 12?

Why vspace-lineskip removes space after tikz picture although it stands before the picture?

Part of my house is inexplicably gone

What is the STRONGEST end-of-line knot to use if you want to use a steel-thimble at the end, so that you've got a steel-eyelet at the end of the line?

What does this line mean in Zelazny's The Courts of Chaos?

How can I find out about the game world without meta-influencing it?

Realistic, logical way for men with medieval-era weaponry to compete with much larger and physically stronger foes

Problem with pronounciation

Does a single fopen introduce TOCTOU vulnerability?

Is Jesus the last Prophet?

Should I list a completely different profession in my technical resume?

How to create two-week recurring alarms and reminders?

Do Veracrypt encrypted volumes have any kind of brute force protection?

C++ logging library

How (un)safe is it to ride barefoot?

Make Gimbap cutter

What does "lit." mean in boiling point or melting point specification?

What's the difference between DHCP and NAT? Are they mutually exclusive?



Savage Road Signs


Cross-road optimization - what is the proper way to solve this type of puzzle?Ernie and the CalendarErnie and the Alien InvasionDroning On in CirclesBuilding a cheap roadErnie and the Grand TourErnie and the slice of PiErnie and the Disco Unicorn4x4 Sliding Puzzle with a twistFinding unique number properties













9












$begingroup$


There is a highway that starts in the city of Savage. You must must place distance marker signs on this highway for the outgoing traffic. According to highway code, there must be a distance marker sign at least every 20 km, and every distance marker sign must be labelled with its distance from the start (the city of Savage).



Normally this isn't a problem for you but there is a snag. Your sign printing machine is broken and your only back-up plan is to steal a pack of stickers from your daughter. This pack of stickers contains ten of each digit, 0 through 9 (that's 100 total stickers). As luck would have it, using these stickers isn't against code and you have plenty of blank signs to put them on.




What is the furthest distance marker sign you can place without breaking highway code?




Note: This isn't meant to be a lateral-thinking question. Use no more than 10 of each digit across all signs, no more than a gap of 20 between signs, the answer is the last sign you place. You do not need leading zeros, so "004" can just be "4".



I do not claim to have the optimal answer (but it's probably pretty good). I did not use a computer program, but they are allowed. I guess if you want to answer you should also list all of your signs? Assuming somebody beats me I'll give out the checkmark after a couple of days.










share|improve this question









$endgroup$











  • $begingroup$
    You mention that this isn't a lateral thinking problem; should I take that to mean that I can't use 6's as 9's and vice versa? (ditto for 2's and 5's, though depending on the font, that's a lot more of a stretch).
    $endgroup$
    – Gilad M
    8 hours ago






  • 1




    $begingroup$
    @GiladM yeah, pretend it's a font where 6's and 9's look different
    $endgroup$
    – Dark Thunder
    7 hours ago















9












$begingroup$


There is a highway that starts in the city of Savage. You must must place distance marker signs on this highway for the outgoing traffic. According to highway code, there must be a distance marker sign at least every 20 km, and every distance marker sign must be labelled with its distance from the start (the city of Savage).



Normally this isn't a problem for you but there is a snag. Your sign printing machine is broken and your only back-up plan is to steal a pack of stickers from your daughter. This pack of stickers contains ten of each digit, 0 through 9 (that's 100 total stickers). As luck would have it, using these stickers isn't against code and you have plenty of blank signs to put them on.




What is the furthest distance marker sign you can place without breaking highway code?




Note: This isn't meant to be a lateral-thinking question. Use no more than 10 of each digit across all signs, no more than a gap of 20 between signs, the answer is the last sign you place. You do not need leading zeros, so "004" can just be "4".



I do not claim to have the optimal answer (but it's probably pretty good). I did not use a computer program, but they are allowed. I guess if you want to answer you should also list all of your signs? Assuming somebody beats me I'll give out the checkmark after a couple of days.










share|improve this question









$endgroup$











  • $begingroup$
    You mention that this isn't a lateral thinking problem; should I take that to mean that I can't use 6's as 9's and vice versa? (ditto for 2's and 5's, though depending on the font, that's a lot more of a stretch).
    $endgroup$
    – Gilad M
    8 hours ago






  • 1




    $begingroup$
    @GiladM yeah, pretend it's a font where 6's and 9's look different
    $endgroup$
    – Dark Thunder
    7 hours ago













9












9








9


1



$begingroup$


There is a highway that starts in the city of Savage. You must must place distance marker signs on this highway for the outgoing traffic. According to highway code, there must be a distance marker sign at least every 20 km, and every distance marker sign must be labelled with its distance from the start (the city of Savage).



Normally this isn't a problem for you but there is a snag. Your sign printing machine is broken and your only back-up plan is to steal a pack of stickers from your daughter. This pack of stickers contains ten of each digit, 0 through 9 (that's 100 total stickers). As luck would have it, using these stickers isn't against code and you have plenty of blank signs to put them on.




What is the furthest distance marker sign you can place without breaking highway code?




Note: This isn't meant to be a lateral-thinking question. Use no more than 10 of each digit across all signs, no more than a gap of 20 between signs, the answer is the last sign you place. You do not need leading zeros, so "004" can just be "4".



I do not claim to have the optimal answer (but it's probably pretty good). I did not use a computer program, but they are allowed. I guess if you want to answer you should also list all of your signs? Assuming somebody beats me I'll give out the checkmark after a couple of days.










share|improve this question









$endgroup$




There is a highway that starts in the city of Savage. You must must place distance marker signs on this highway for the outgoing traffic. According to highway code, there must be a distance marker sign at least every 20 km, and every distance marker sign must be labelled with its distance from the start (the city of Savage).



Normally this isn't a problem for you but there is a snag. Your sign printing machine is broken and your only back-up plan is to steal a pack of stickers from your daughter. This pack of stickers contains ten of each digit, 0 through 9 (that's 100 total stickers). As luck would have it, using these stickers isn't against code and you have plenty of blank signs to put them on.




What is the furthest distance marker sign you can place without breaking highway code?




Note: This isn't meant to be a lateral-thinking question. Use no more than 10 of each digit across all signs, no more than a gap of 20 between signs, the answer is the last sign you place. You do not need leading zeros, so "004" can just be "4".



I do not claim to have the optimal answer (but it's probably pretty good). I did not use a computer program, but they are allowed. I guess if you want to answer you should also list all of your signs? Assuming somebody beats me I'll give out the checkmark after a couple of days.







mathematics combinatorics






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked 9 hours ago









Dark ThunderDark Thunder

818114




818114











  • $begingroup$
    You mention that this isn't a lateral thinking problem; should I take that to mean that I can't use 6's as 9's and vice versa? (ditto for 2's and 5's, though depending on the font, that's a lot more of a stretch).
    $endgroup$
    – Gilad M
    8 hours ago






  • 1




    $begingroup$
    @GiladM yeah, pretend it's a font where 6's and 9's look different
    $endgroup$
    – Dark Thunder
    7 hours ago
















  • $begingroup$
    You mention that this isn't a lateral thinking problem; should I take that to mean that I can't use 6's as 9's and vice versa? (ditto for 2's and 5's, though depending on the font, that's a lot more of a stretch).
    $endgroup$
    – Gilad M
    8 hours ago






  • 1




    $begingroup$
    @GiladM yeah, pretend it's a font where 6's and 9's look different
    $endgroup$
    – Dark Thunder
    7 hours ago















$begingroup$
You mention that this isn't a lateral thinking problem; should I take that to mean that I can't use 6's as 9's and vice versa? (ditto for 2's and 5's, though depending on the font, that's a lot more of a stretch).
$endgroup$
– Gilad M
8 hours ago




$begingroup$
You mention that this isn't a lateral thinking problem; should I take that to mean that I can't use 6's as 9's and vice versa? (ditto for 2's and 5's, though depending on the font, that's a lot more of a stretch).
$endgroup$
– Gilad M
8 hours ago




1




1




$begingroup$
@GiladM yeah, pretend it's a font where 6's and 9's look different
$endgroup$
– Dark Thunder
7 hours ago




$begingroup$
@GiladM yeah, pretend it's a font where 6's and 9's look different
$endgroup$
– Dark Thunder
7 hours ago










2 Answers
2






active

oldest

votes


















3












$begingroup$

Edit: my improved answer is




688 km


Stepping by 19 or 20 km gives


20 40 60 80 99 118 137 157 177 197 217 237 256 276 295 314 334 353 372 392 411 430 450 470 490 509 529 549 569 588 608 628 648 668 688




My (previous) answer is




488 km.


20 40 60 80 100 120 140 160 180 199 219 239 259 279 299 319 338 358 378 398 418 438 457 477 488


The signs go every 20km until I run out of 0s.

The next is after 19km, and again every 20 km until I run out of 9s.

The next is after 19km, and again every 20 km until I run out of 8s.

The next is after 19km, and again every 20 km until the furthest sign I can make within 20 km

— there are no 8s (48x) or 9s (49x) or 0s (50x) left.







share|improve this answer











$endgroup$












  • $begingroup$
    It seems to be beneficial to preserve some of the 0s until later on. Even though Gilad M has made an error, with a slight correction, they can still get easily over 600.
    $endgroup$
    – hexomino
    6 hours ago










  • $begingroup$
    @hexomino yes I noticed that: deleting the last two terms beats this. I decided to post something after the false start from another answer (too many zeros) although I feel this could be better.
    $endgroup$
    – Weather Vane
    6 hours ago










  • $begingroup$
    Yeah, sorry, fixed now, I think. Listen, counting is hard. :P
    $endgroup$
    – Gilad M
    6 hours ago










  • $begingroup$
    @hexomino I found a way to improve the answer.
    $endgroup$
    – Weather Vane
    6 hours ago






  • 1




    $begingroup$
    The new solution is neat! It uses all 100 digits exactly!
    $endgroup$
    – Dr Xorile
    6 hours ago


















2












$begingroup$


646 km




I'm not sure this is the best answer, but I think it's close, and at the very least some decent headway for someone who didn't feel like writing a script to solve it.



To start:




I came up with a hard limit: what if you could just put signs every 20 km without worrying which digits were repeated? Then you'd spend 10 digits getting up to 100 km, and another 15 for each 100 km past that. That gets us to 700 km at the very most. We know the answer's not getting past that. (Actually you could probably get to 710 or 720 with some shenanigans involving high numbers with 1 fewer digit, like 9 and 99, but I digress. My answer doesn't really care about off-by-one errors like that).




So now that we know that




we have no chance of using lots of 7's, 8's, 9's, and 0's in a row, we realize that these digits are a lot less valuable to us than the 1's through 5's that we'll need when we get a few hundred kilometers out.




Next,




I assumed the answer was close to optimal, so 600-something. I'll need 5, maybe 6 each of digits 1 through 5 just for hundreds places. If I'm climbing by just under 20 at a time, I'll need a bunch of odd digits for tens places, and then at some point I'll run out and need to switch to evens. Every switch is a loss of efficiency, so I'll try to only do it once. The rest of the digits will be used for the ones places. That's the game plan.




Following that plan, here's what I came up with:




20, 40, 60, 80, 100, 120, 133, 141, 159, 179, 199, 219, 239, 259, 279, 299, 317, 337, 357, 373, 388, 408, 428, 448, 468, 488, 507, 527, 547, 567, 586, 606, 626, 646.




I could keep rearranging things, but




given that all I have left after this sequence are two 5's, and we're pretty damn close to the fundamental maximum of 700, I think this is close enough. If this isn't the answer, I'm pretty sure that the real answer is ~670, but not much more than that.







share|improve this answer











$endgroup$












  • $begingroup$
    There are only 10 of each digit available.
    $endgroup$
    – Weather Vane
    7 hours ago










  • $begingroup$
    ...I only used 10 of each digit, I'm pretty sure. Did I miss something? If this is about the first sequence that used an extra 0, I fixed that in my final answer.
    $endgroup$
    – Gilad M
    7 hours ago











  • $begingroup$
    Counting them??
    $endgroup$
    – Weather Vane
    7 hours ago






  • 1




    $begingroup$
    5 is used 12 times: 159, 259, 357, 507, 527, 547, 566, 586, 605, 625, 645, 665.
    $endgroup$
    – hexomino
    7 hours ago






  • 2




    $begingroup$
    ...which is a shame, because I really liked the "one kilometer short of hell" line :P
    $endgroup$
    – Gilad M
    6 hours ago











Your Answer








StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "559"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);













draft saved

draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f84904%2fsavage-road-signs%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown

























2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes









3












$begingroup$

Edit: my improved answer is




688 km


Stepping by 19 or 20 km gives


20 40 60 80 99 118 137 157 177 197 217 237 256 276 295 314 334 353 372 392 411 430 450 470 490 509 529 549 569 588 608 628 648 668 688




My (previous) answer is




488 km.


20 40 60 80 100 120 140 160 180 199 219 239 259 279 299 319 338 358 378 398 418 438 457 477 488


The signs go every 20km until I run out of 0s.

The next is after 19km, and again every 20 km until I run out of 9s.

The next is after 19km, and again every 20 km until I run out of 8s.

The next is after 19km, and again every 20 km until the furthest sign I can make within 20 km

— there are no 8s (48x) or 9s (49x) or 0s (50x) left.







share|improve this answer











$endgroup$












  • $begingroup$
    It seems to be beneficial to preserve some of the 0s until later on. Even though Gilad M has made an error, with a slight correction, they can still get easily over 600.
    $endgroup$
    – hexomino
    6 hours ago










  • $begingroup$
    @hexomino yes I noticed that: deleting the last two terms beats this. I decided to post something after the false start from another answer (too many zeros) although I feel this could be better.
    $endgroup$
    – Weather Vane
    6 hours ago










  • $begingroup$
    Yeah, sorry, fixed now, I think. Listen, counting is hard. :P
    $endgroup$
    – Gilad M
    6 hours ago










  • $begingroup$
    @hexomino I found a way to improve the answer.
    $endgroup$
    – Weather Vane
    6 hours ago






  • 1




    $begingroup$
    The new solution is neat! It uses all 100 digits exactly!
    $endgroup$
    – Dr Xorile
    6 hours ago















3












$begingroup$

Edit: my improved answer is




688 km


Stepping by 19 or 20 km gives


20 40 60 80 99 118 137 157 177 197 217 237 256 276 295 314 334 353 372 392 411 430 450 470 490 509 529 549 569 588 608 628 648 668 688




My (previous) answer is




488 km.


20 40 60 80 100 120 140 160 180 199 219 239 259 279 299 319 338 358 378 398 418 438 457 477 488


The signs go every 20km until I run out of 0s.

The next is after 19km, and again every 20 km until I run out of 9s.

The next is after 19km, and again every 20 km until I run out of 8s.

The next is after 19km, and again every 20 km until the furthest sign I can make within 20 km

— there are no 8s (48x) or 9s (49x) or 0s (50x) left.







share|improve this answer











$endgroup$












  • $begingroup$
    It seems to be beneficial to preserve some of the 0s until later on. Even though Gilad M has made an error, with a slight correction, they can still get easily over 600.
    $endgroup$
    – hexomino
    6 hours ago










  • $begingroup$
    @hexomino yes I noticed that: deleting the last two terms beats this. I decided to post something after the false start from another answer (too many zeros) although I feel this could be better.
    $endgroup$
    – Weather Vane
    6 hours ago










  • $begingroup$
    Yeah, sorry, fixed now, I think. Listen, counting is hard. :P
    $endgroup$
    – Gilad M
    6 hours ago










  • $begingroup$
    @hexomino I found a way to improve the answer.
    $endgroup$
    – Weather Vane
    6 hours ago






  • 1




    $begingroup$
    The new solution is neat! It uses all 100 digits exactly!
    $endgroup$
    – Dr Xorile
    6 hours ago













3












3








3





$begingroup$

Edit: my improved answer is




688 km


Stepping by 19 or 20 km gives


20 40 60 80 99 118 137 157 177 197 217 237 256 276 295 314 334 353 372 392 411 430 450 470 490 509 529 549 569 588 608 628 648 668 688




My (previous) answer is




488 km.


20 40 60 80 100 120 140 160 180 199 219 239 259 279 299 319 338 358 378 398 418 438 457 477 488


The signs go every 20km until I run out of 0s.

The next is after 19km, and again every 20 km until I run out of 9s.

The next is after 19km, and again every 20 km until I run out of 8s.

The next is after 19km, and again every 20 km until the furthest sign I can make within 20 km

— there are no 8s (48x) or 9s (49x) or 0s (50x) left.







share|improve this answer











$endgroup$



Edit: my improved answer is




688 km


Stepping by 19 or 20 km gives


20 40 60 80 99 118 137 157 177 197 217 237 256 276 295 314 334 353 372 392 411 430 450 470 490 509 529 549 569 588 608 628 648 668 688




My (previous) answer is




488 km.


20 40 60 80 100 120 140 160 180 199 219 239 259 279 299 319 338 358 378 398 418 438 457 477 488


The signs go every 20km until I run out of 0s.

The next is after 19km, and again every 20 km until I run out of 9s.

The next is after 19km, and again every 20 km until I run out of 8s.

The next is after 19km, and again every 20 km until the furthest sign I can make within 20 km

— there are no 8s (48x) or 9s (49x) or 0s (50x) left.








share|improve this answer














share|improve this answer



share|improve this answer








edited 6 hours ago

























answered 7 hours ago









Weather VaneWeather Vane

3,8121118




3,8121118











  • $begingroup$
    It seems to be beneficial to preserve some of the 0s until later on. Even though Gilad M has made an error, with a slight correction, they can still get easily over 600.
    $endgroup$
    – hexomino
    6 hours ago










  • $begingroup$
    @hexomino yes I noticed that: deleting the last two terms beats this. I decided to post something after the false start from another answer (too many zeros) although I feel this could be better.
    $endgroup$
    – Weather Vane
    6 hours ago










  • $begingroup$
    Yeah, sorry, fixed now, I think. Listen, counting is hard. :P
    $endgroup$
    – Gilad M
    6 hours ago










  • $begingroup$
    @hexomino I found a way to improve the answer.
    $endgroup$
    – Weather Vane
    6 hours ago






  • 1




    $begingroup$
    The new solution is neat! It uses all 100 digits exactly!
    $endgroup$
    – Dr Xorile
    6 hours ago
















  • $begingroup$
    It seems to be beneficial to preserve some of the 0s until later on. Even though Gilad M has made an error, with a slight correction, they can still get easily over 600.
    $endgroup$
    – hexomino
    6 hours ago










  • $begingroup$
    @hexomino yes I noticed that: deleting the last two terms beats this. I decided to post something after the false start from another answer (too many zeros) although I feel this could be better.
    $endgroup$
    – Weather Vane
    6 hours ago










  • $begingroup$
    Yeah, sorry, fixed now, I think. Listen, counting is hard. :P
    $endgroup$
    – Gilad M
    6 hours ago










  • $begingroup$
    @hexomino I found a way to improve the answer.
    $endgroup$
    – Weather Vane
    6 hours ago






  • 1




    $begingroup$
    The new solution is neat! It uses all 100 digits exactly!
    $endgroup$
    – Dr Xorile
    6 hours ago















$begingroup$
It seems to be beneficial to preserve some of the 0s until later on. Even though Gilad M has made an error, with a slight correction, they can still get easily over 600.
$endgroup$
– hexomino
6 hours ago




$begingroup$
It seems to be beneficial to preserve some of the 0s until later on. Even though Gilad M has made an error, with a slight correction, they can still get easily over 600.
$endgroup$
– hexomino
6 hours ago












$begingroup$
@hexomino yes I noticed that: deleting the last two terms beats this. I decided to post something after the false start from another answer (too many zeros) although I feel this could be better.
$endgroup$
– Weather Vane
6 hours ago




$begingroup$
@hexomino yes I noticed that: deleting the last two terms beats this. I decided to post something after the false start from another answer (too many zeros) although I feel this could be better.
$endgroup$
– Weather Vane
6 hours ago












$begingroup$
Yeah, sorry, fixed now, I think. Listen, counting is hard. :P
$endgroup$
– Gilad M
6 hours ago




$begingroup$
Yeah, sorry, fixed now, I think. Listen, counting is hard. :P
$endgroup$
– Gilad M
6 hours ago












$begingroup$
@hexomino I found a way to improve the answer.
$endgroup$
– Weather Vane
6 hours ago




$begingroup$
@hexomino I found a way to improve the answer.
$endgroup$
– Weather Vane
6 hours ago




1




1




$begingroup$
The new solution is neat! It uses all 100 digits exactly!
$endgroup$
– Dr Xorile
6 hours ago




$begingroup$
The new solution is neat! It uses all 100 digits exactly!
$endgroup$
– Dr Xorile
6 hours ago











2












$begingroup$


646 km




I'm not sure this is the best answer, but I think it's close, and at the very least some decent headway for someone who didn't feel like writing a script to solve it.



To start:




I came up with a hard limit: what if you could just put signs every 20 km without worrying which digits were repeated? Then you'd spend 10 digits getting up to 100 km, and another 15 for each 100 km past that. That gets us to 700 km at the very most. We know the answer's not getting past that. (Actually you could probably get to 710 or 720 with some shenanigans involving high numbers with 1 fewer digit, like 9 and 99, but I digress. My answer doesn't really care about off-by-one errors like that).




So now that we know that




we have no chance of using lots of 7's, 8's, 9's, and 0's in a row, we realize that these digits are a lot less valuable to us than the 1's through 5's that we'll need when we get a few hundred kilometers out.




Next,




I assumed the answer was close to optimal, so 600-something. I'll need 5, maybe 6 each of digits 1 through 5 just for hundreds places. If I'm climbing by just under 20 at a time, I'll need a bunch of odd digits for tens places, and then at some point I'll run out and need to switch to evens. Every switch is a loss of efficiency, so I'll try to only do it once. The rest of the digits will be used for the ones places. That's the game plan.




Following that plan, here's what I came up with:




20, 40, 60, 80, 100, 120, 133, 141, 159, 179, 199, 219, 239, 259, 279, 299, 317, 337, 357, 373, 388, 408, 428, 448, 468, 488, 507, 527, 547, 567, 586, 606, 626, 646.




I could keep rearranging things, but




given that all I have left after this sequence are two 5's, and we're pretty damn close to the fundamental maximum of 700, I think this is close enough. If this isn't the answer, I'm pretty sure that the real answer is ~670, but not much more than that.







share|improve this answer











$endgroup$












  • $begingroup$
    There are only 10 of each digit available.
    $endgroup$
    – Weather Vane
    7 hours ago










  • $begingroup$
    ...I only used 10 of each digit, I'm pretty sure. Did I miss something? If this is about the first sequence that used an extra 0, I fixed that in my final answer.
    $endgroup$
    – Gilad M
    7 hours ago











  • $begingroup$
    Counting them??
    $endgroup$
    – Weather Vane
    7 hours ago






  • 1




    $begingroup$
    5 is used 12 times: 159, 259, 357, 507, 527, 547, 566, 586, 605, 625, 645, 665.
    $endgroup$
    – hexomino
    7 hours ago






  • 2




    $begingroup$
    ...which is a shame, because I really liked the "one kilometer short of hell" line :P
    $endgroup$
    – Gilad M
    6 hours ago















2












$begingroup$


646 km




I'm not sure this is the best answer, but I think it's close, and at the very least some decent headway for someone who didn't feel like writing a script to solve it.



To start:




I came up with a hard limit: what if you could just put signs every 20 km without worrying which digits were repeated? Then you'd spend 10 digits getting up to 100 km, and another 15 for each 100 km past that. That gets us to 700 km at the very most. We know the answer's not getting past that. (Actually you could probably get to 710 or 720 with some shenanigans involving high numbers with 1 fewer digit, like 9 and 99, but I digress. My answer doesn't really care about off-by-one errors like that).




So now that we know that




we have no chance of using lots of 7's, 8's, 9's, and 0's in a row, we realize that these digits are a lot less valuable to us than the 1's through 5's that we'll need when we get a few hundred kilometers out.




Next,




I assumed the answer was close to optimal, so 600-something. I'll need 5, maybe 6 each of digits 1 through 5 just for hundreds places. If I'm climbing by just under 20 at a time, I'll need a bunch of odd digits for tens places, and then at some point I'll run out and need to switch to evens. Every switch is a loss of efficiency, so I'll try to only do it once. The rest of the digits will be used for the ones places. That's the game plan.




Following that plan, here's what I came up with:




20, 40, 60, 80, 100, 120, 133, 141, 159, 179, 199, 219, 239, 259, 279, 299, 317, 337, 357, 373, 388, 408, 428, 448, 468, 488, 507, 527, 547, 567, 586, 606, 626, 646.




I could keep rearranging things, but




given that all I have left after this sequence are two 5's, and we're pretty damn close to the fundamental maximum of 700, I think this is close enough. If this isn't the answer, I'm pretty sure that the real answer is ~670, but not much more than that.







share|improve this answer











$endgroup$












  • $begingroup$
    There are only 10 of each digit available.
    $endgroup$
    – Weather Vane
    7 hours ago










  • $begingroup$
    ...I only used 10 of each digit, I'm pretty sure. Did I miss something? If this is about the first sequence that used an extra 0, I fixed that in my final answer.
    $endgroup$
    – Gilad M
    7 hours ago











  • $begingroup$
    Counting them??
    $endgroup$
    – Weather Vane
    7 hours ago






  • 1




    $begingroup$
    5 is used 12 times: 159, 259, 357, 507, 527, 547, 566, 586, 605, 625, 645, 665.
    $endgroup$
    – hexomino
    7 hours ago






  • 2




    $begingroup$
    ...which is a shame, because I really liked the "one kilometer short of hell" line :P
    $endgroup$
    – Gilad M
    6 hours ago













2












2








2





$begingroup$


646 km




I'm not sure this is the best answer, but I think it's close, and at the very least some decent headway for someone who didn't feel like writing a script to solve it.



To start:




I came up with a hard limit: what if you could just put signs every 20 km without worrying which digits were repeated? Then you'd spend 10 digits getting up to 100 km, and another 15 for each 100 km past that. That gets us to 700 km at the very most. We know the answer's not getting past that. (Actually you could probably get to 710 or 720 with some shenanigans involving high numbers with 1 fewer digit, like 9 and 99, but I digress. My answer doesn't really care about off-by-one errors like that).




So now that we know that




we have no chance of using lots of 7's, 8's, 9's, and 0's in a row, we realize that these digits are a lot less valuable to us than the 1's through 5's that we'll need when we get a few hundred kilometers out.




Next,




I assumed the answer was close to optimal, so 600-something. I'll need 5, maybe 6 each of digits 1 through 5 just for hundreds places. If I'm climbing by just under 20 at a time, I'll need a bunch of odd digits for tens places, and then at some point I'll run out and need to switch to evens. Every switch is a loss of efficiency, so I'll try to only do it once. The rest of the digits will be used for the ones places. That's the game plan.




Following that plan, here's what I came up with:




20, 40, 60, 80, 100, 120, 133, 141, 159, 179, 199, 219, 239, 259, 279, 299, 317, 337, 357, 373, 388, 408, 428, 448, 468, 488, 507, 527, 547, 567, 586, 606, 626, 646.




I could keep rearranging things, but




given that all I have left after this sequence are two 5's, and we're pretty damn close to the fundamental maximum of 700, I think this is close enough. If this isn't the answer, I'm pretty sure that the real answer is ~670, but not much more than that.







share|improve this answer











$endgroup$




646 km




I'm not sure this is the best answer, but I think it's close, and at the very least some decent headway for someone who didn't feel like writing a script to solve it.



To start:




I came up with a hard limit: what if you could just put signs every 20 km without worrying which digits were repeated? Then you'd spend 10 digits getting up to 100 km, and another 15 for each 100 km past that. That gets us to 700 km at the very most. We know the answer's not getting past that. (Actually you could probably get to 710 or 720 with some shenanigans involving high numbers with 1 fewer digit, like 9 and 99, but I digress. My answer doesn't really care about off-by-one errors like that).




So now that we know that




we have no chance of using lots of 7's, 8's, 9's, and 0's in a row, we realize that these digits are a lot less valuable to us than the 1's through 5's that we'll need when we get a few hundred kilometers out.




Next,




I assumed the answer was close to optimal, so 600-something. I'll need 5, maybe 6 each of digits 1 through 5 just for hundreds places. If I'm climbing by just under 20 at a time, I'll need a bunch of odd digits for tens places, and then at some point I'll run out and need to switch to evens. Every switch is a loss of efficiency, so I'll try to only do it once. The rest of the digits will be used for the ones places. That's the game plan.




Following that plan, here's what I came up with:




20, 40, 60, 80, 100, 120, 133, 141, 159, 179, 199, 219, 239, 259, 279, 299, 317, 337, 357, 373, 388, 408, 428, 448, 468, 488, 507, 527, 547, 567, 586, 606, 626, 646.




I could keep rearranging things, but




given that all I have left after this sequence are two 5's, and we're pretty damn close to the fundamental maximum of 700, I think this is close enough. If this isn't the answer, I'm pretty sure that the real answer is ~670, but not much more than that.








share|improve this answer














share|improve this answer



share|improve this answer








edited 6 hours ago

























answered 8 hours ago









Gilad MGilad M

1837




1837











  • $begingroup$
    There are only 10 of each digit available.
    $endgroup$
    – Weather Vane
    7 hours ago










  • $begingroup$
    ...I only used 10 of each digit, I'm pretty sure. Did I miss something? If this is about the first sequence that used an extra 0, I fixed that in my final answer.
    $endgroup$
    – Gilad M
    7 hours ago











  • $begingroup$
    Counting them??
    $endgroup$
    – Weather Vane
    7 hours ago






  • 1




    $begingroup$
    5 is used 12 times: 159, 259, 357, 507, 527, 547, 566, 586, 605, 625, 645, 665.
    $endgroup$
    – hexomino
    7 hours ago






  • 2




    $begingroup$
    ...which is a shame, because I really liked the "one kilometer short of hell" line :P
    $endgroup$
    – Gilad M
    6 hours ago
















  • $begingroup$
    There are only 10 of each digit available.
    $endgroup$
    – Weather Vane
    7 hours ago










  • $begingroup$
    ...I only used 10 of each digit, I'm pretty sure. Did I miss something? If this is about the first sequence that used an extra 0, I fixed that in my final answer.
    $endgroup$
    – Gilad M
    7 hours ago











  • $begingroup$
    Counting them??
    $endgroup$
    – Weather Vane
    7 hours ago






  • 1




    $begingroup$
    5 is used 12 times: 159, 259, 357, 507, 527, 547, 566, 586, 605, 625, 645, 665.
    $endgroup$
    – hexomino
    7 hours ago






  • 2




    $begingroup$
    ...which is a shame, because I really liked the "one kilometer short of hell" line :P
    $endgroup$
    – Gilad M
    6 hours ago















$begingroup$
There are only 10 of each digit available.
$endgroup$
– Weather Vane
7 hours ago




$begingroup$
There are only 10 of each digit available.
$endgroup$
– Weather Vane
7 hours ago












$begingroup$
...I only used 10 of each digit, I'm pretty sure. Did I miss something? If this is about the first sequence that used an extra 0, I fixed that in my final answer.
$endgroup$
– Gilad M
7 hours ago





$begingroup$
...I only used 10 of each digit, I'm pretty sure. Did I miss something? If this is about the first sequence that used an extra 0, I fixed that in my final answer.
$endgroup$
– Gilad M
7 hours ago













$begingroup$
Counting them??
$endgroup$
– Weather Vane
7 hours ago




$begingroup$
Counting them??
$endgroup$
– Weather Vane
7 hours ago




1




1




$begingroup$
5 is used 12 times: 159, 259, 357, 507, 527, 547, 566, 586, 605, 625, 645, 665.
$endgroup$
– hexomino
7 hours ago




$begingroup$
5 is used 12 times: 159, 259, 357, 507, 527, 547, 566, 586, 605, 625, 645, 665.
$endgroup$
– hexomino
7 hours ago




2




2




$begingroup$
...which is a shame, because I really liked the "one kilometer short of hell" line :P
$endgroup$
– Gilad M
6 hours ago




$begingroup$
...which is a shame, because I really liked the "one kilometer short of hell" line :P
$endgroup$
– Gilad M
6 hours ago

















draft saved

draft discarded
















































Thanks for contributing an answer to Puzzling Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid


  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f84904%2fsavage-road-signs%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







Popular posts from this blog

19. јануар Садржај Догађаји Рођења Смрти Празници и дани сећања Види још Референце Мени за навигацијуу

Israel Cuprins Etimologie | Istorie | Geografie | Politică | Demografie | Educație | Economie | Cultură | Note explicative | Note bibliografice | Bibliografie | Legături externe | Meniu de navigaresite web oficialfacebooktweeterGoogle+Instagramcanal YouTubeInstagramtextmodificaremodificarewww.technion.ac.ilnew.huji.ac.ilwww.weizmann.ac.ilwww1.biu.ac.ilenglish.tau.ac.ilwww.haifa.ac.ilin.bgu.ac.ilwww.openu.ac.ilwww.ariel.ac.ilCIA FactbookHarta Israelului"Negotiating Jerusalem," Palestine–Israel JournalThe Schizoid Nature of Modern Hebrew: A Slavic Language in Search of a Semitic Past„Arabic in Israel: an official language and a cultural bridge”„Latest Population Statistics for Israel”„Israel Population”„Tables”„Report for Selected Countries and Subjects”Human Development Report 2016: Human Development for Everyone„Distribution of family income - Gini index”The World FactbookJerusalem Law„Israel”„Israel”„Zionist Leaders: David Ben-Gurion 1886–1973”„The status of Jerusalem”„Analysis: Kadima's big plans”„Israel's Hard-Learned Lessons”„The Legacy of Undefined Borders, Tel Aviv Notes No. 40, 5 iunie 2002”„Israel Journal: A Land Without Borders”„Population”„Israel closes decade with population of 7.5 million”Time Series-DataBank„Selected Statistics on Jerusalem Day 2007 (Hebrew)”Golan belongs to Syria, Druze protestGlobal Survey 2006: Middle East Progress Amid Global Gains in FreedomWHO: Life expectancy in Israel among highest in the worldInternational Monetary Fund, World Economic Outlook Database, April 2011: Nominal GDP list of countries. Data for the year 2010.„Israel's accession to the OECD”Popular Opinion„On the Move”Hosea 12:5„Walking the Bible Timeline”„Palestine: History”„Return to Zion”An invention called 'the Jewish people' – Haaretz – Israel NewsoriginalJewish and Non-Jewish Population of Palestine-Israel (1517–2004)ImmigrationJewishvirtuallibrary.orgChapter One: The Heralders of Zionism„The birth of modern Israel: A scrap of paper that changed history”„League of Nations: The Mandate for Palestine, 24 iulie 1922”The Population of Palestine Prior to 1948originalBackground Paper No. 47 (ST/DPI/SER.A/47)History: Foreign DominationTwo Hundred and Seventh Plenary Meeting„Israel (Labor Zionism)”Population, by Religion and Population GroupThe Suez CrisisAdolf EichmannJustice Ministry Reply to Amnesty International Report„The Interregnum”Israel Ministry of Foreign Affairs – The Palestinian National Covenant- July 1968Research on terrorism: trends, achievements & failuresThe Routledge Atlas of the Arab–Israeli conflict: The Complete History of the Struggle and the Efforts to Resolve It"George Habash, Palestinian Terrorism Tactician, Dies at 82."„1973: Arab states attack Israeli forces”Agranat Commission„Has Israel Annexed East Jerusalem?”original„After 4 Years, Intifada Still Smolders”From the End of the Cold War to 2001originalThe Oslo Accords, 1993Israel-PLO Recognition – Exchange of Letters between PM Rabin and Chairman Arafat – Sept 9- 1993Foundation for Middle East PeaceSources of Population Growth: Total Israeli Population and Settler Population, 1991–2003original„Israel marks Rabin assassination”The Wye River Memorandumoriginal„West Bank barrier route disputed, Israeli missile kills 2”"Permanent Ceasefire to Be Based on Creation Of Buffer Zone Free of Armed Personnel Other than UN, Lebanese Forces"„Hezbollah kills 8 soldiers, kidnaps two in offensive on northern border”„Olmert confirms peace talks with Syria”„Battleground Gaza: Israeli ground forces invade the strip”„IDF begins Gaza troop withdrawal, hours after ending 3-week offensive”„THE LAND: Geography and Climate”„Area of districts, sub-districts, natural regions and lakes”„Israel - Geography”„Makhteshim Country”Israel and the Palestinian Territories„Makhtesh Ramon”„The Living Dead Sea”„Temperatures reach record high in Pakistan”„Climate Extremes In Israel”Israel in figures„Deuteronom”„JNF: 240 million trees planted since 1901”„Vegetation of Israel and Neighboring Countries”Environmental Law in Israel„Executive branch”„Israel's election process explained”„The Electoral System in Israel”„Constitution for Israel”„All 120 incoming Knesset members”„Statul ISRAEL”„The Judiciary: The Court System”„Israel's high court unique in region”„Israel and the International Criminal Court: A Legal Battlefield”„Localities and population, by population group, district, sub-district and natural region”„Israel: Districts, Major Cities, Urban Localities & Metropolitan Areas”„Israel-Egypt Relations: Background & Overview of Peace Treaty”„Solana to Haaretz: New Rules of War Needed for Age of Terror”„Israel's Announcement Regarding Settlements”„United Nations Security Council Resolution 497”„Security Council resolution 478 (1980) on the status of Jerusalem”„Arabs will ask U.N. to seek razing of Israeli wall”„Olmert: Willing to trade land for peace”„Mapping Peace between Syria and Israel”„Egypt: Israel must accept the land-for-peace formula”„Israel: Age structure from 2005 to 2015”„Global, regional, and national disability-adjusted life years (DALYs) for 306 diseases and injuries and healthy life expectancy (HALE) for 188 countries, 1990–2013: quantifying the epidemiological transition”10.1016/S0140-6736(15)61340-X„World Health Statistics 2014”„Life expectancy for Israeli men world's 4th highest”„Family Structure and Well-Being Across Israel's Diverse Population”„Fertility among Jewish and Muslim Women in Israel, by Level of Religiosity, 1979-2009”„Israel leaders in birth rate, but poverty major challenge”„Ethnic Groups”„Israel's population: Over 8.5 million”„Israel - Ethnic groups”„Jews, by country of origin and age”„Minority Communities in Israel: Background & Overview”„Israel”„Language in Israel”„Selected Data from the 2011 Social Survey on Mastery of the Hebrew Language and Usage of Languages”„Religions”„5 facts about Israeli Druze, a unique religious and ethnic group”„Israël”Israel Country Study Guide„Haredi city in Negev – blessing or curse?”„New town Harish harbors hopes of being more than another Pleasantville”„List of localities, in alphabetical order”„Muncitorii români, doriți în Israel”„Prietenia româno-israeliană la nevoie se cunoaște”„The Higher Education System in Israel”„Middle East”„Academic Ranking of World Universities 2016”„Israel”„Israel”„Jewish Nobel Prize Winners”„All Nobel Prizes in Literature”„All Nobel Peace Prizes”„All Prizes in Economic Sciences”„All Nobel Prizes in Chemistry”„List of Fields Medallists”„Sakharov Prize”„Țara care și-a sfidat "destinul" și se bate umăr la umăr cu Silicon Valley”„Apple's R&D center in Israel grew to about 800 employees”„Tim Cook: Apple's Herzliya R&D center second-largest in world”„Lecții de economie de la Israel”„Land use”Israel Investment and Business GuideA Country Study: IsraelCentral Bureau of StatisticsFlorin Diaconu, „Kadima: Flexibilitate și pragmatism, dar nici un compromis în chestiuni vitale", în Revista Institutului Diplomatic Român, anul I, numărul I, semestrul I, 2006, pp. 71-72Florin Diaconu, „Likud: Dreapta israeliană constant opusă retrocedării teritoriilor cureite prin luptă în 1967", în Revista Institutului Diplomatic Român, anul I, numărul I, semestrul I, 2006, pp. 73-74MassadaIsraelul a crescut in 50 de ani cât alte state intr-un mileniuIsrael Government PortalIsraelIsraelIsraelmmmmmXX451232cb118646298(data)4027808-634110000 0004 0372 0767n7900328503691455-bb46-37e3-91d2-cb064a35ffcc1003570400564274ge1294033523775214929302638955X146498911146498911

Smell Mother Skizze Discussion Tachometer Jar Alligator Star 끌다 자세 의문 과학적t Barbaric The round system critiques the connection. Definition: A wind instrument of music in use among the Spaniards Nasty Level 이상 분노 금년 월급 근교 Cloth Owner Permissible Shock Purring Parched Raise 오전 장면 햄 서투르다 The smash instructs the squeamish instrument. Large Nosy Nalpure Chalk Travel Crayon Bite your tongue The Hulk 신호 대사 사과하다 The work boosts the knowledgeable size. Steeplump Level Wooden Shake Teaching Jump 이제 복도 접다 공중전화 부지런하다 Rub Average Ruthless Busyglide Glost oven Didelphia Control A fly on the wall Jaws 지하철 거