### 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.

# School Dinners

##### Stage: 3 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

Our school dinners offer the same basic choice each day.

Starter: soup or fruit juice;
Main course: meat, fish, salad, chicken or curry;
Dessert: crumble, cake or sponge

I change my choice for each course every day, trying each option in turn, going back to soup after fruit juice, to meat after curry and to crumble after sponge. Today, I shall sit down to soup, meat and crumble.

How many school dinners will I have eaten before I next sit down to the same combination?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.