### Counting on Letters

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

### Magic Caterpillars

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

### Plum Tree

Label this plum tree graph to make it totally magic!

# Product Sudoku 2

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

Produced by Henry Kwok

#### The Basic Rules of Diagonal Product Sudoku

Like the standard Sudoku, this Sudoku consists of a grid of nine rows and nine columns subdivided into nine 3x3 subgrids. Like the standard Sudoku, it 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 small numbers written after the double slash marks on the intersections between cells.
Each clue-number is the product of the two digits in the two cells 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, //24 in the bottom left box means that possible pairs of numbers for cells (3,7) and cell (2,8) are either 3 and 8, 8 and 3; 4 and 6, or 6 and 4 respectively. Similarly, \\18 in the middle right box means that possible pairs of numbers in the cells (8,5) (9,6) are either 2 and 9, 9 and 2; 3 and 6, or 6 and 3 respectively.

A word document containing the problem can be found here, for use in the classroom.