**Today’s Challenge**

Consider all whole numbers from 1 to 60, then delete the following:

- all prime numbers,
- any number that differs by 1 from a prime,
- all square numbers,
- any number that differs by 1 from a square,
- all multiples of 5,
- any number that differs by 1 from a multiple of 5,
- all multiples of 7,
- any number that differs by 1 from a multiple of 7.

One number should remain, what is it?

**The 7puzzle Challenge**

The playing board of **the 7puzzle game** is a 7-by-7 grid containing 49 different numbers, ranging from **2 **up to **84**.

The 1st & 7th rows of the playing board contain the following fourteen numbers:

2 4 9 11 14 15 22 24 27 30 40 70 72 77

What is the difference between the highest prime number and highest square number?

**Make 20 Challenge**

Can you arrive at 20 by inserting 1, 4, 6 and 8 into the gaps on each line?

- (◯–◯)×(◯–◯) = 20
- (◯÷◯+◯)×◯ = 20
- (◯+◯)×◯–◯ = 20

**Answers **can be found **here**.

**Click Paul Godding for details of online maths tuition. Wherever you are in the world, please get in touch.**