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

A palindromic number is a number that can be read the same forwards and backwards (e.g. 333 and 797). How many palindromic numbers are there between **100 and 1,000**?

**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 contain the following fourteen numbers:

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

What is the sum of the 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 SIX ways of making **124 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **4** and **12 **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 **124** by inserting **5**, **8**, **10** and **16** into the gaps on each line?

- (◯+◯)×◯+√◯ = 124
- ◯×◯–(◯÷◯)² = 124
- (◯–◯÷◯)×◯ = 124

**An****swers **can be found **here**.

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