These are the answers to the puzzles which appeared in this blog post.
|3||9||1||multiple of 17|
|7||2||5||multiple of 25|
|4||8||6||multiple of 9|
|multiple of 11||multiple of 16||multiple of 12|
|3||2||multiple of 8|
|prime||multiple of 4|
No two digit prime number can end in 5 (as it would be divisible by 5). Therefore the 5 must go here:
However, there are only two prime numbers beginning with a 5: 53 and 59. 9 is not available, so only 53 is allowed. But to complete the grid, two primes beginning with 5 must be formed.
Therefore it is impossible to complete the grid.
There are 22 ways to do this (or 11 if you ignore reflections).
Similar puzzles can be formed from non-square grids, like these:
There are two ways to do this:
As every two or more digit prime number is odd, the squares marked with a * must be odd:
1, 3, 5 and 7 are the only available odd digits, so one of these four square must contain a 5. This however means that one of the numbers formed ends in a 5 and so is not prime.
Therefore it is impossible.
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