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

Another mini-**Mathelona** challenge where your task is to correctly place the eight digits **1 1 1 2 2 3 4 **and **5** into the eight gaps so both lines work out arithmetically:

◯ + ◯ = 3 = ◯ – ◯

◯ + ◯ = 4 = ◯ × ◯

Click **Mathelona** for details of our popular pocket book of challenges.

**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 1st & 4th rows contain the following fourteen numbers:

2 3 9 10 14 15 22 32 35 40 44 54 60 72

Which five numbers listed can be made by adding two others from the list?

**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 FOUR ways of making **144 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using the three digits **2**, **6** and **9** once each, with + – × ÷ available, which are the only THREE numbers it’s possible to make from the list below?

7 14 21 28 35 42 49 56 63 70

#*7TimesTable*

**The Target Challenge**

Can you arrive at **144** by inserting **4**, **6**, **9** and **12** into the gaps on each line?

- ◯×◯×(◯–◯) = 144
- ◯×◯×double(◯–◯) = 144
- ◯×◯×(◯÷◯)² = 144
- ◯²×(◯+◯–◯) = 144 (2 different ways!)
- ◯×◯+treble(◯×√◯) = 144

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

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