# Answers to puzzles on square grids

These are the answers to the puzzles which appeared in this blog post.

### 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

### 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.

These are the answers to the puzzles which appeared in this blog post.

### 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

### 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. Matthew is a postdoctoral researcher at the University of Cambridge. He hasn’t had time to play Klax since the noughties, but he’s pretty sure that Coke is it!