**T****h****e Main Challenge**

One of our easier **Mathelona**-style challenges, still utilising the four arithmetic operations. Place the eight digits **1 2 2 3 4 4 5** and **6** into the gaps so both lines work out:

◯ + ◯ = 6 = ◯ × ◯

◯ – ◯ = 2 = ◯ ÷ ◯

If you enjoy this type of number puzzle, click **Mathelona** for details of our 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

What is the difference between the two multiples of 7?

**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 SIX ways of making **141 **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 is possible to make from the list below?

4 8 12 16 20 24 28 32 36 40

#*4TimesTable*

**The Target Challenge**

Can you arrive at **141** by inserting **3**, **5**, **7** and **12** into the gaps on each line?

- ◯×(◯+◯)–◯ = 141
- (◯×◯+◯)×◯ = 141
- ◯³+◯+◯–◯ = 141

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

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