One-digit products in a row of numbersCan you fill a 3x3 grid with these numbers so the products of the rows...
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One-digit products in a row of numbers
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$begingroup$
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 10 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 10 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 10 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 10 hours ago
ThomasLThomasL
7902 silver badges19 bronze badges
edited 9 hours ago
JMP
25.8k6 gold badges49 silver badges111 bronze badges
asked 10 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 10 hours ago
ThomasLThomasL
7902 silver badges19 bronze badges
asked 10 hours ago
ThomasLThomasL
7902 silver badges19 bronze badges
asked 10 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 9 hours ago
Arnaud MortierArnaud Mortier
5,77413 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
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2 Answers
2
active
oldest
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active
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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 9 hours ago
Arnaud MortierArnaud Mortier
5,77413 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 9 hours ago
Arnaud MortierArnaud Mortier
5,77413 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 9 hours ago
Arnaud MortierArnaud Mortier
5,77413 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 9 hours ago
Arnaud MortierArnaud Mortier
5,77413 silver badges49 bronze badges
edited 8 hours ago
answered 9 hours ago
Arnaud MortierArnaud Mortier
5,77413 silver badges49 bronze badges
answered 9 hours ago
Arnaud MortierArnaud Mortier
5,77413 silver badges49 bronze badges
answered 9 hours ago
Arnaud MortierArnaud Mortier
5,77413 silver badges49 bronze badges
5,77413 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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