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

When multiplying two numbers together and then adding or subtracting a third number, there are four ways of reaching **60** when the three numbers used in each calculation are in the range **1-9**, and can be repeated.

One way to make 60 is (9×6)+6; can you find the other three?

[Note: (9×6)+6 and (6×9)+6 counts as just one way.]

**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 & 5th rows contain the following fourteen numbers:

6 7 13 16 21 25 36 42 45 50 66 80 81 84

How many pairs of consecutive numbers are there?

**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 SIX ways of making **66 **when using *Lagrange’s Theorem*. Can you find them all?

**The Mathematically Possible Challenge**

Using **4**, **6** and **12 **once each, with + – × ÷ available, which SIX numbers is it possible to make from the list below?

3 6 9 12 15 18 21 24 27 30

#*3TimesTable*

**The Target Challenge**

Can you arrive at **66** by inserting **2**, **3**, **4** and **9** into the gaps on each line?

- (◯×◯+◯)×◯ = 66
- (◯×◯–◯)×◯ = 66
- ◯²×◯+◯×◯ = 66
- ◯³+(◯+◯)²+√◯ = 66

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

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