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

Here’s another 10-step question involving all four arithmetic operations and all numbers from **1 to 10**.

Start with the number **28**, then:

- divide by four
- multiply by six
- subtract two
- add five
- divide by nine
- multiply by one
- add ten
- divide by three
- add eight
- subtract seven

What is your answer?

**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 difference between the sum of the multiples of 11 and the sum of the prime numbers?

**T****he Lagrange Challenge**

*Lagrange’s Four-Square Theorem* states that every 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).

Show how you can make **186**, in NINE different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Using **3**, **6** and **12** once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

2 3 5 7 11 13 17 19 23 29

#*PrimeNumbers*

**The Target ****Challeng****e**

Can you arrive at **186** by inserting **3**, **4**, **6** and **9** into the gaps on each line?

- (◯×◯+◯)×◯ = 186
- (◯×◯+double◯)×◯ = 186

**An****swers **can be found **here**.

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