### Month Mania

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

### Doodles

A 'doodle' is a closed intersecting curve drawn without taking pencil from paper. Only two lines cross at each intersection or vertex (never 3), that is the vertex points must be 'double points' not 'triple points'. Number the vertex points in any order. Starting at any point on the doodle, trace it until you get back to where you started. Write down the numbers of the vertices as you pass through them. So you have a [not necessarily unique] list of numbers for each doodle. Prove that 1)each vertex number in a list occurs twice. [easy!] 2)between each pair of vertex numbers in a list there are an even number of other numbers [hard!]

### Euler's Officers

How many different solutions can you find to this problem? Arrange 25 officers, each having one of five different ranks a, b, c, d and e, and belonging to one of five different regiments p, q, r, s and t, in a square formation 5 by 5, so that each row and each file contains just one officer of each rank and just one from each regiment. There is an interactive version of this problem.

# Diagonal Sums Sudoku

##### Stage: 2, 3 and 4 Challenge Level:

 5 1 3 9 6 2 7 8 4 4 8 6 7 3 5 1 2 9 7 2 9 8 1 4 6 3 5 8 6 5 2 7 9 3 4 1 1 7 4 6 5 3 2 9 8 3 9 2 1 4 8 5 6 7 9 5 8 3 2 7 4 1 6 2 4 1 5 8 6 9 7 3 6 3 7 4 9 1 8 5 2