**The Main Challenge**

Your task is to arrive at the target answer of **7** by using each of the numbers **0.7**, **2**, **7** and **10** exactly once each, 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 4th & 7th rows contain the following fourteen numbers:

3 4 10 11 24 27 30 32 35 44 54 60 70 77

How many multiples of 3 are present?

**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 **185**, in EIGHT different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

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

1 3 6 10 15 21 28 36 45 55 66

#*TriangularNumbers*

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

Can you arrive at **185** by inserting **5**, **15**, **20** and **30** into the gaps on each line?

- ◯+◯×◯+◯ = 185
- ◯×(◯–◯)–half◯ = 185

**Answers **can be found **here**.

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