**The Main Challenge**

You have been given the task of manually numbering a 100-page document from 1 to 100. What is the total of all the individual digits written?

**T****he**** 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 1st & 6th rows contain the following fourteen numbers:

2 5 9 12 14 15 18 20 22 33 40 49 56 72

Find three pairs of numbers that each have a sum of 42.

**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** (or 4+1+1+1).

Show how you can make **176**, in TWO different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **3**, **6** and **12** once each, with + – × ÷ available, which THREE target numbers is it possible to make from the list below?

4 8 12 16 20 24 28 32 36 40

#*4TimesTable*

**The Target Challeng****e**

Can you arrive at **176** by inserting **6**, **7**, **8** and **9** into the gaps on each line?

- (◯+◯+◯)×◯ = 176
- ◯²+◯²+◯²–treble◯ = 176

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

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