### Ewa's Eggs

I put eggs into a basket in groups of 7 and noticed that I could easily have divided them into piles of 2, 3, 4, 5 or 6 and always have one left over. How many eggs were in the basket?

### Inclusion Exclusion

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

### Cogs

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the cogwheel A as the wheels rotate.

# A First Product Sudoku

##### Stage: 3 Challenge Level:

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 (3x3 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 on the intersections between two cells. Each clue-number is the product of the two digits in the two cells that are on either side of it.

For example, 8 in the top right box means that possible pairs of numbers for the cells above and below are either 1 and 8, 8 and 1, 4 and 2, or 2 and 4 respectively.

A word document containing the Sudoku problem can be found here