# School Dinners

Our school dinners offer the same choice each day, and each day I try a new option. How long will it be before I eat the same meal again?

## Problem

Our school dinners offer the same basic choice each day.

Starter: soup or salad;

Main course: pasta, fishcakes, pizza, burger or curry;

Dessert: crumble, cake or fruit salad

I change my choice for each course every day, trying each option in turn, going back to soup after salad, to pasta after curry and to crumble after fruit salad.

Today, I shall sit down to soup, pasta and crumble.

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

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

## Student Solutions

Every second meal I will have soup for my starter.

Every $5$th meal I will have pasta for my main course.

Every $3$rd meal I will have crumble for my dessert.

$2, 5$, and $3$ have no common factors, so I will have eaten $2\times5\times3=30$ school dinners (the Lowest Common Multiple) before I sit down to the same combination again.