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

Can you arrive at the target answer of **24** by using the digits **2**, **9**, **13** and **13** exactly once each and with + – × ÷ available?

**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 1st & 6th rows contain the following fourteen numbers:

2 5 9 12 14 15 18 20 22 33 40 49 56 72

Which three numbers, when each is multiplied by 4, have their answers on the list?

**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 FIVE ways of making **74 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **4**, **6** and **12 **once each, with + – × ÷ available, which THREE numbers are not possible to make from the list below?

12 24 36 48 60 72 84 96 108 120

#*12TimesTable*

**The Target Challenge**

Can you arrive at **74** by inserting **4**, **6**, **7** and **8** into the gaps on each line?

- ◯×◯+◯×◯ = 74
- (◯+◯)×◯–◯² = 74
- (◯+◯)×◯+◯ = 74

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

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