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

Your task is to multiply two numbers together and then subtract a third number to achieve the target answer of **7**. The three numbers used in each calculation must all be unique digits from **1-9**.

For example, one such way of making **7** is (4×3)–5. Can you find SIX other ways to make 7?

[Note: (4×3)–5 = 7 and (3×4)–5 = 7 counts as ONE way.]

**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 5th & 6th rows contain the following fourteen numbers:

5 6 7 12 16 18 20 21 33 49 50 56 81 84

What is the difference between the total of the prime numbers and the sum of the multiples of 10?

**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 is only ONE way of making **15 **when using *Lagrange’s Theorem*. Can you find it?

**The Mathematically Possible Challenge**

Using **5**, **6** and **8 **once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

5 10 15 20 25 30 35 40 45 50

#*5TimesTable*

**The Target Challenge**

Can you arrive at **15** by inserting **2**, **3**, **5** and **6** into the gaps on each line?

- ◯×◯+◯–◯ = 15
- ◯÷◯×◯²×◯ = 15
- ◯²–(◯+◯)×◯ = 15

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

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