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

You roll two normal six-sided dice, both containing the numbers **1-6**. When multiplying the two numbers that show, how many DIFFERENT answers is it possible to obtain?

**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 & 7th rows contain the following fourteen numbers:

4 11 13 24 25 27 30 36 42 45 66 70 77 80

What is the sum of the factors of 90?

**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 FOUR ways of making **49 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **8**, **9** and **10 **once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

10 20 30 40 50 60 70 80 90 100

#*10TimesTables*

**The Target Challenge**

Can you arrive at **49** by inserting **1**, **2**, **3** and **4** into the gaps on each line?

- (◯+◯)²×(◯–◯)² = 49
- (◯+◯)²×√◯–◯ = 49
- ◯⁶–(◯+◯)×◯ = 49

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

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