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

Can you insert the numbers **0 to 9 **exactly TWICE each into the gaps below so all five lines work out arithmetically?

◯ + ◯ = 15 = ◯ + ◯

◯ + ◯ = 5 = ◯ – ◯

◯ + ◯ = 10 = ◯ × ◯

◯ – ◯ = 2 = ◯ ÷ ◯

◯ + ◯ = 9 = ◯ × ◯

If you enjoyed attempting this, click this **Mathelona** link for details of our slightly easier pocket book 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 3rd & 6th rows contain the following fourteen numbers:

5 12 13 18 20 25 33 36 42 45 49 56 66 80

What is the sum of the numbers in the 40’s?

**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 FIVE ways of making **131 **when using *Lagrange’s Theorem*. Can you find them all?

**The Mathematically Possible Challenge**

Using **3**, **6** and **10 **once each, with + – × ÷ available, which SIX numbers is it possible to make from the list below?

6 12 18 24 30 36 42 48 54 60

#*6TimesTable*

**The Target Challenge**

Can you arrive at **131** by inserting **4**, **5**, **7** and **9** into the gaps on each line?

- ◯×◯×◯–◯ = 131
- ◯×◯×√◯+◯ = 131

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

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