**T****h****e Main Challenge**

Which is the only digit not represented when listing the square numbers from **10² to 19²**?

**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

Find three different numbers that have a sum of 100.

**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 FOUR ways of making **63 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

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

1 4 9 16 25 36 49 64 81 100

#*SquareNumbers*

**The Target Challenge**

Can you arrive at **63** by inserting **3**, **3**, **4** and **5** into the gaps on each line?

- ◯×◯×◯+◯ = 63
- ◯²×◯–◯×◯ = 63
- ◯×◯×(◯+√◯) = 63

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

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