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.