**The Main Challenge**

Try the following number challenge similar to the ones found in our **Mathelona** pocket book of challenges. Click the link for details.

Your task is to make all four lines below work arithmetically by placing the following 16 digits into the 16 gaps.

0 0 1 1 2 2 4 4 5 5 6 6 7 7 8 9

◯ + ◯ = 15 = ◯ + ◯

◯ + ◯ = 2 = ◯ – ◯

◯ + ◯ = 8 = ◯ × ◯

◯ + ◯ = 1 = ◯ ÷ ◯

It’s tricky – but can you do it?

**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 sum of the multiples of 16?

**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 **188**, in FIVE different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **3**, **4** and **12** once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

5 10 15 20 25 30 35 40 45 50

#*5TimesTabl**e*

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

Can you arrive at **188** by inserting **2**, **9**, **10** and **11** into the gaps on each line?

- ◯×◯×◯–◯ = 188
- (◯×◯–half◯)×◯ = 188
- (◯+◯)×◯–half◯ = 188

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

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