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One-digit products in a row of numbers
Can you fill a 3x3 grid with these numbers so the products of the rows and columns are the same?Increasing rows and columnsWhat is my four digit car number?Four-by-four table with equal row and column products90s Number PuzzleIn a square, arrange the binary numbers such that no $n$:th digit is the same along a row or columnThree-digit multiplication puzzle, part III: Return of the HexHow do I make numbers 50-100 using only the numbers 2, 0, 1, 9?Squares inside a square
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
The digits from 1 to 9 can be arranged in a row, such that any two
neighbouring digits in this row is the product of two one-digit numbers.
Arrangement:
$$728163549$$
Is it possible to do such an arrangement using hexadecimal digits 1-9 and A-F?
Here the row has 15 digits and all numbers are treated as hexadecimal numbers.
Example: 123456789ABCDEF
12=2*9, 23=5*7, 34=4*D, 45 does not work, etc.
mathematics calculation-puzzle
edited 9 hours ago
JMP
25.8k6 gold badges49 silver badges111 bronze badges
asked 9 hours ago
ThomasLThomasL
7902 silver badges19 bronze badges
$endgroup$
add a comment
|
$begingroup$
The digits from 1 to 9 can be arranged in a row, such that any two
neighbouring digits in this row is the product of two one-digit numbers.
Arrangement:
$$728163549$$
Is it possible to do such an arrangement using hexadecimal digits 1-9 and A-F?
Here the row has 15 digits and all numbers are treated as hexadecimal numbers.
Example: 123456789ABCDEF
12=2*9, 23=5*7, 34=4*D, 45 does not work, etc.
mathematics calculation-puzzle
edited 9 hours ago
JMP
25.8k6 gold badges49 silver badges111 bronze badges
asked 9 hours ago
ThomasLThomasL
7902 silver badges19 bronze badges
$endgroup$
add a comment
|
$begingroup$
The digits from 1 to 9 can be arranged in a row, such that any two
neighbouring digits in this row is the product of two one-digit numbers.
Arrangement:
$$728163549$$
Is it possible to do such an arrangement using hexadecimal digits 1-9 and A-F?
Here the row has 15 digits and all numbers are treated as hexadecimal numbers.
Example: 123456789ABCDEF
12=2*9, 23=5*7, 34=4*D, 45 does not work, etc.
mathematics calculation-puzzle
edited 9 hours ago
JMP
25.8k6 gold badges49 silver badges111 bronze badges
asked 9 hours ago
ThomasLThomasL
7902 silver badges19 bronze badges
$endgroup$
The digits from 1 to 9 can be arranged in a row, such that any two
neighbouring digits in this row is the product of two one-digit numbers.
Arrangement:
$$728163549$$
Is it possible to do such an arrangement using hexadecimal digits 1-9 and A-F?
Here the row has 15 digits and all numbers are treated as hexadecimal numbers.
Example: 123456789ABCDEF
12=2*9, 23=5*7, 34=4*D, 45 does not work, etc.
mathematics calculation-puzzle
mathematics calculation-puzzle
edited 9 hours ago
JMP
25.8k6 gold badges49 silver badges111 bronze badges
asked 9 hours ago
ThomasLThomasL
7902 silver badges19 bronze badges
edited 9 hours ago
JMP
25.8k6 gold badges49 silver badges111 bronze badges
asked 9 hours ago
ThomasLThomasL
7902 silver badges19 bronze badges
edited 9 hours ago
JMP
25.8k6 gold badges49 silver badges111 bronze badges
edited 9 hours ago
JMP
25.8k6 gold badges49 silver badges111 bronze badges
edited 9 hours ago
JMP
25.8k6 gold badges49 silver badges111 bronze badges
25.8k6 gold badges49 silver badges111 bronze badges
asked 9 hours ago
ThomasLThomasL
7902 silver badges19 bronze badges
asked 9 hours ago
ThomasLThomasL
7902 silver badges19 bronze badges
asked 9 hours ago
ThomasLThomasL
7902 silver badges19 bronze badges
7902 silver badges19 bronze badges
add a comment
|
add a comment
|
2 Answers
2
active
oldest
votes
$begingroup$
One solution is
$$D2379A5B6C4E18F$$
Thought process:
No product starts with $F$, so $F$ must be at the end, and the only options are $3F$ and $8F$.
The only $2$-digit numbers that are products of $1$-digit number and start with digits $A, B, C, D, E$ are $$A5, A8, A9, B4, B6, C3, C4, D2, E1.$$
Therefore we must have subsequences $E1$ and $D2$.
From this, you quickly get an answer by looking at the above table. I don't know if I was lucky, but apart from the observations above, I guessed all the rest right. Just for the sake of it, here is another one: $$D24E1879A5B6C3F$$
answered 8 hours ago
Arnaud MortierArnaud Mortier
5,76913 silver badges49 bronze badges
$endgroup$
add a comment
|
$begingroup$
As an addendum to the answer from @Arnaud:
The smallest such number is 375B6E19C4D2A8F.
According to the brute-force program I made, there are just $787$ solutions.
answered 8 hours ago
JensJens
3966 bronze badges
$endgroup$
add a comment
|
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
One solution is
$$D2379A5B6C4E18F$$
Thought process:
No product starts with $F$, so $F$ must be at the end, and the only options are $3F$ and $8F$.
The only $2$-digit numbers that are products of $1$-digit number and start with digits $A, B, C, D, E$ are $$A5, A8, A9, B4, B6, C3, C4, D2, E1.$$
Therefore we must have subsequences $E1$ and $D2$.
From this, you quickly get an answer by looking at the above table. I don't know if I was lucky, but apart from the observations above, I guessed all the rest right. Just for the sake of it, here is another one: $$D24E1879A5B6C3F$$
answered 8 hours ago
Arnaud MortierArnaud Mortier
5,76913 silver badges49 bronze badges
$endgroup$
add a comment
|
$begingroup$
One solution is
$$D2379A5B6C4E18F$$
Thought process:
No product starts with $F$, so $F$ must be at the end, and the only options are $3F$ and $8F$.
The only $2$-digit numbers that are products of $1$-digit number and start with digits $A, B, C, D, E$ are $$A5, A8, A9, B4, B6, C3, C4, D2, E1.$$
Therefore we must have subsequences $E1$ and $D2$.
From this, you quickly get an answer by looking at the above table. I don't know if I was lucky, but apart from the observations above, I guessed all the rest right. Just for the sake of it, here is another one: $$D24E1879A5B6C3F$$
answered 8 hours ago
Arnaud MortierArnaud Mortier
5,76913 silver badges49 bronze badges
$endgroup$
add a comment
|
$begingroup$
One solution is
$$D2379A5B6C4E18F$$
Thought process:
No product starts with $F$, so $F$ must be at the end, and the only options are $3F$ and $8F$.
The only $2$-digit numbers that are products of $1$-digit number and start with digits $A, B, C, D, E$ are $$A5, A8, A9, B4, B6, C3, C4, D2, E1.$$
Therefore we must have subsequences $E1$ and $D2$.
From this, you quickly get an answer by looking at the above table. I don't know if I was lucky, but apart from the observations above, I guessed all the rest right. Just for the sake of it, here is another one: $$D24E1879A5B6C3F$$
answered 8 hours ago
Arnaud MortierArnaud Mortier
5,76913 silver badges49 bronze badges
$endgroup$
One solution is
$$D2379A5B6C4E18F$$
Thought process:
No product starts with $F$, so $F$ must be at the end, and the only options are $3F$ and $8F$.
The only $2$-digit numbers that are products of $1$-digit number and start with digits $A, B, C, D, E$ are $$A5, A8, A9, B4, B6, C3, C4, D2, E1.$$
Therefore we must have subsequences $E1$ and $D2$.
From this, you quickly get an answer by looking at the above table. I don't know if I was lucky, but apart from the observations above, I guessed all the rest right. Just for the sake of it, here is another one: $$D24E1879A5B6C3F$$
answered 8 hours ago
Arnaud MortierArnaud Mortier
5,76913 silver badges49 bronze badges
edited 8 hours ago
answered 8 hours ago
Arnaud MortierArnaud Mortier
5,76913 silver badges49 bronze badges
answered 8 hours ago
Arnaud MortierArnaud Mortier
5,76913 silver badges49 bronze badges
answered 8 hours ago
Arnaud MortierArnaud Mortier
5,76913 silver badges49 bronze badges
5,76913 silver badges49 bronze badges
add a comment
|
add a comment
|
$begingroup$
As an addendum to the answer from @Arnaud:
The smallest such number is 375B6E19C4D2A8F.
According to the brute-force program I made, there are just $787$ solutions.
answered 8 hours ago
JensJens
3966 bronze badges
$endgroup$
add a comment
|
$begingroup$
As an addendum to the answer from @Arnaud:
The smallest such number is 375B6E19C4D2A8F.
According to the brute-force program I made, there are just $787$ solutions.
answered 8 hours ago
JensJens
3966 bronze badges
$endgroup$
add a comment
|
$begingroup$
As an addendum to the answer from @Arnaud:
The smallest such number is 375B6E19C4D2A8F.
According to the brute-force program I made, there are just $787$ solutions.
answered 8 hours ago
JensJens
3966 bronze badges
$endgroup$
As an addendum to the answer from @Arnaud:
The smallest such number is 375B6E19C4D2A8F.
According to the brute-force program I made, there are just $787$ solutions.
answered 8 hours ago
JensJens
3966 bronze badges
edited 8 hours ago
answered 8 hours ago
JensJens
3966 bronze badges
answered 8 hours ago
JensJens
3966 bronze badges
answered 8 hours ago
JensJens
3966 bronze badges
3966 bronze badges
add a comment
|
add a comment
|
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