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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

Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections? ### Euler's Officers

How many different ways can you arrange the officers in a square?

# Diagonal Sums Sudoku

#### by Henry Kwok ### Rules of Diagonal Sums Sudoku

Like the standard Sudoku, this Sudoku has two basic rules:
1. Each column, each row and each box (3$\times$3 subgrid) must have the numbers 1 to 9.
2. No column, row or box can have two squares with the same number.
The puzzle can be solved with the help of clue-numbers which are written after slash marks on the intersections of border lines. Each clue-number is the sum of two digits in the two squares that are diagonally adjacent to each other. The position of each pair of diagonally adjacent squares is indicated by either two forward slash marks // or two backward slash marks \\.

For example, the //12 on the border of the top right hand box means that possible pairs of numbers in the cells above-right and below left are:
3 and 9, 9 and 3; 4 and 8, 8 and 4; 5 and 7, or 7 and 5 respectively.

Similarly, the \\6 in the bottom left box means that possible pairs of numbers in the cells above-left and below-right are:
1 and 5, 5 and 1; 2 and 4, or 4 and 2 respectively.