**T**** h****e Ma****in Challenge**

This is very famous in Japan, having been an integral part of a TV advert for Google’s Nexus 7 tablet a few years ago. Click this YouTube link for a browse.

Using the numbers **1**, **1**, **5** and **8** exactly once each, with + – × and ÷ available, can you beat this tricky Japanese challenge by arriving at the target answer of **10**?

**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 more square numbers than prime numbers are listed above?

**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 NINE different ways to make **209 **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 TWO numbers it is possible to make from the list below?

2 3 5 7 11 13 17 19 23 29

#*PrimeNumbers*

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

Can you arrive at **209** by inserting **2**, **7**, **9** and **12** into the gaps on each line?

- ◯×◯×◯–◯ = 209
- (◯+◯)×(◯+◯) = 209

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

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