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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.
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