**The Main Challenge**

Find the sum of the numbers that remain after eliminating multiples of 3, 5 and 7 from all the odd numbers between 10 and 40.

**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 2nd & 6th rows of the playing board contain the following fourteen numbers:

5 8 12 17 18 20 28 33 48 49 55 56 63 64

From the list, which three different numbers have a sum of 100?

**The Lagrange Challenge**

*Lagrange’s Four-Square Theorem* states that every integer can be made by adding up to four square numbers.

For example, **7** can be made by **2²+1²+1²+1²** (4+1+1+1).

Show how you can make **150**, in ELEVEN different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using the three digits **2**, **6** and **9** once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

1 8 27 64 125

#*CubeNumbers*

**The Target Challenge**

Can you arrive at **150** by inserting **10**, **20**, **25** and **30** into the gaps on each line?

- (◯+◯)×(◯–◯) = 150
- ◯×◯–double(◯+◯) = 150

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

**Click Paul Godding for details of online maths tuition.**