**T**** he Main Challenge**

When listing the FIVE 3-digit cube numbers, all digits from **1 to 9** are represented, except one. Which digit is missing?

**The**** 7puzzle Challenge**

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

The 2nd & 7th rows contain the following fourteen numbers:

4 8 11 17 24 27 28 30 48 55 63 64 70 77

What is the difference between the two multiples of 9?

**The Lagrange Challenge**

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

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

There are THREE ways of making **62 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **1**, **6** and **7 **once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

9 18 27 36 45 54 63 72 81 90

#*9TimesTable*

**The Target Challenge**

Can you arrive at **62** by inserting **2**, **4**, **6** and **9** into the gaps on each line?

- (◯+◯)×◯+◯ = 62
- (◯+◯)×◯–◯ = 62
- (◯+◯)×◯+◯² = 62

**A****nswers **can be found **here**.

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