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

Try the following **Mathelona** challenge, similar to my pocket book challenges but slightly tougher!

Your task is to make all four lines work out arithmetically by placing the 16 digits listed below into the 16 gaps. Can you achieve it?

0 0 1 1 2 2 3 3 4 4 5 6 6 7 8 9

◯ + ◯ = 8 = ◯ + ◯

◯ + ◯ = 7 = ◯ – ◯

◯ + ◯ = 6 = ◯ × ◯

◯ + ◯ = 4 = ◯ ÷ ◯

Full details can be found at **Mathelona**.

**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 2nd & 5th rows of the playing board contain the following fourteen numbers:

6 7 8 16 17 21 28 48 50 55 63 64 81 84

How many factors does the smallest number in the list have?

**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).

There are SIXTEEN different ways to make **210 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

Using **5**, **7** and **11 **once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

1 3 5 7 9 11 13 15 17 19

#*OddNumbers*

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

Can you arrive at **210** by inserting **5**, **10**, **12** and **18** into the gaps on each line?

- ◯×◯+◯×◯ = 210
- (◯–◯÷◯)×◯ = 210

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

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