Fruit line-up
This grocer wants to arrange his fruit in a particular order, can you help him?
Age
11 to 14
Challenge level
Problem
A grocer places some oranges, peaches, apples and bananas in a row so that somewhere in the row, each type of fruit can be found next to each other type of fruit.
What is the smallest possible number of fruits in the row?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 8
Each fruit type needs to touch all of the other three types, but each fruit can only be next to two other fruits.
So there must be at least 2 fruits of every type $\Rightarrow$ at least 8 fruits altogether.
Find an arrangement with 8 fruits to show that this is possible:
OABPOBAP (O for Orange, P for Peach, A for Apple, B for Banana).