Related Collections

Consecutive Numbers

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

Have You Got It?

Can you explain the strategy for winning this game with any target?

Counting Factors

Is there an efficient way to work out how many factors a large number has?

Halloween Day

Age 11 to 14 Short
Challenge Level

October has 31 days so, in any year, in October there are three days of the week which occur five times and four days which occur four times.

As there were exactly four Tuesdays and exactly four Fridays, there could not have been five Wednesdays or five Thursdays, so the days which occurred five times were Saturday, Sunday and Monday.

Hence October 1st fell on a Saturday, which means that October 31st was a Monday.

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.