These are the answers to the puzzles which appeared in this blog post.
3×3 Grids
Puzzle #1
| 4 | 5 | 8 | even |
| 6 | 1 | 3 | prime |
| 7 | 2 | 9 | cube |
| prime | cube | prime |
Puzzle #2
| 3 | 8 | 9 | emirp |
| 4 | 2 | 6 | even |
| 7 | 5 | 1 | emirp |
| emirp | odd | square |
Puzzle #3
| 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 |
Puzzle #4
| 4 | 6 | 3 | prime |
| 8 | 2 | 9 | prime |
| 7 | 5 | 1 | prime |
| prime | square | prime |
2×2 Grids
Puzzle #5
| 4 | 1 | prime |
| 3 | 2 | multiple of 8 |
| prime | multiple of 4 |
Puzzle #6
No two digit prime number can end in 5 (as it would be divisible by 5). Therefore the 5 must go here:
| 5 | prime | |
| prime | ||
| prime | prime |
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.
Puzzle #7
There are 22 ways to do this (or 11 if you ignore reflections).
And Finally…
Similar puzzles can be formed from non-square grids, like these:
Puzzle #8
There are two ways to do this:
| 1 | 7 | prime | |
| 5 | 9 | 3 | prime |
| prime | prime | prime |
| 7 | 1 | prime | |
| 5 | 9 | 3 | prime |
| prime | prime | prime |
Puzzle #9
As every two or more digit prime number is odd, the squares marked with a * must be odd:
| * | prime | |||
| * | * | * | prime | |
| prime | prime | prime | prime |
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.
More from Chalkdust
Crossnumber winners, Issues 18 & 19
Did you solve it?Crossnumber winners, Issue 17
Did you solve it?Crossnumber winners, Issue 16
Did you solve it?Prize crossnumber, Issue 16
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Cryptic crossword, Issue 16
Can you solve it?Crossnumber winners, Issue 15
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