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

When allocating each letter of the English alphabet a numerical value as follows; **A=1 B=2** **C=3 … Z=26**, the value of the word SUM, for example, would be 19+21+13 = 53.

What would be the value of our popular number puzzle, **MATHELONA**?

**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 3rd & 5th rows contain the following fourteen numbers:

6 7 13 16 21 25 36 42 45 50 66 80 81 84

Find three pairs of numbers that have a sum that is also on the list.

**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 **173**, in SEVEN different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Using **4**, **6** and **10** once each, with + – × ÷ available, which THREE target numbers is it possible to make from the list below?

1 8 27 64 125

#*CubeNumber*s

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

Can you arrive at **173** by inserting **5**, **7**, **14** and **15** into the gaps on each line?

- (◯×◯)+(◯×◯) = 173
- ◯×(◯+◯)–half◯ = 173

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

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