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...

Regional Division

Stage: 3 Short Challenge Level: Challenge Level:1

the answerSome trial and error will produce a solution like that on the right, where there are $9$ different areas enclosed.

To see that this is indeed the maximum, there is always one central region ($9$ on the diagram), and then the others must be separated from this by one of the sides of one of the rectangles. Each side can only separate one region, and as there are a total of $8$ sides, this means at most $9$ regions in total.

This problem is taken from the UKMT Mathematical Challenges.