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?
Age
11 to 14
Challenge level
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.