Our school dinners offer the same basic choice each day.
Starters: soup or fruit juice;
Main course: meat, fish, salad, chicken or curry;
Afters: 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.