**T**** he Main Challenge**

Using each of the four numbers **0.8**, **0.9**, **1.5** and **5** once each, and with the four arithmetical operations + – × ÷ available to use, can you arrive at the target answer of **7**?

**The**** 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 2nd & 3rd rows contain the following fourteen numbers:

8 13 17 25 28 36 42 45 48 55 63 64 66 80

What is the sum of the prime numbers?

**The 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 SEVEN ways of making **82 **when using *Lagrange’s Theorem*. Can you find them all?

**The Mathematically Possible Challenge**

Using **2**, **3** and **11 **once each, with + – × ÷ available, which THREE numbers are possible to make from the list below?

7 14 21 28 35 42 49 56 63 70

#*7TimesTable*

**The Target Challenge**

Can you arrive at **82** by inserting **1**, **8**, **9** and **10** into the gaps on each line?

- ◯×◯–◯×◯ = 82
- ◯²+◯+◯–◯ = 82
- ◯×◯+√◯–√◯ = 82
- ◯×◯×◯+◯ = 82

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

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