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

In this *Kakuro*-style question, can you list the ONLY way possible to make **16** when adding together five unique digits from **1-9**?

**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 4th & 5th rows of the playing board contain the following fourteen numbers:

3 6 7 10 16 21 32 35 44 50 54 60 81 84

How many pairs of numbers differ by exactly 10?

**T****he 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).

Show how you can make **195**, in TEN different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Using **3**, **4** and **12** once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

1 8 27 64 125

#*CubeNumbers*

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

Can you arrive at **195** by inserting **5**, **8**, **13** and **18** into the gaps on each line?

- (◯+◯+◯)×◯ = 195
- (◯+◯–◯)×◯ = 195

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

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