You may also like

problem icon

Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

problem icon

Calendar Capers

Choose any three by three square of dates on a calendar page...

problem icon

Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Fruit Line-up

Stage: 3 Short Challenge Level: Challenge Level:1

Each fruit can have at most two fruits next to it but each type of fruit must be next to three other types of fruit so there are at least two of every fruit. This means there are at least $8$ fruits in total. In fact $8$ are sufficient, as shown in the arrangement
 
OABPOBAP (O for Orange, P for Peach, A for Apple, B for Banana)
 

 

This problem is taken from the UKMT Mathematical Challenges.