Mr.P’s Parent Maths Problem of the Week

Hello parents,

Last week’s parent problem asked you to identify the pattern behind a set of “sums of consecutive odd numbers”. The key idea was to notice that the total depends on how many odd numbers are being added. If there are ‘n’ odd numbers in the sum, then the total is simply n².

For example, the sum 1 + 3 + 5 + 7 + 9 contains five odd numbers. Squaring 5 gives 25, which is exactly the result of adding those numbers together.

Using the same pattern, consider the sum of all the odd numbers up to 95 + 97 + 99. There are 50 odd numbers between 1 and 99, so the total is 50² = 2500.

Well done to everyone who solved it!

Solutions will be published in the following week’s edition of the Barrow Hills Bulletin.

Problem 5: 6 February 2026
There’s a fun maths problem called the handshake problem. If 10 people at an event have to shake hands with every other person, how many handshakes will occur? The answer, of course, is 45. 

This week’s question reverses this handshake problem: 

If 105 handshakes take place, then how many people are at the event?