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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?

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Inclusion Exclusion

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

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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: Challenge Level:1
Rosie and Zoe solved this Sudoku, their journey can be found here. The order with which they filled the Sudoku is marked in the boxes. This is one possible method of many to help you solve the problem.