**The Main Challenge**

Can you place the 12 digits 0, 1, 1, 2, 3, 4, 5, 5, 6, 7, 9 and 9 into the gaps below so that all three lines work out arithmetically?

◯ + ◯ = 4 = ◯ – ◯

◯ + ◯ = 18 = ◯ × ◯

◯ + ◯ = 7 = ◯ ÷ ◯

To order a pocket book full of these popular number puzzles, click **Mathelona**.

**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

Which two numbers, when each is doubled, become cube numbers?

**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 **182**, 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 THREE target numbers is it possible to make from the list below?

10 20 30 40 50 60 70 80 90 100

#*10TimesTable*

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

Can you arrive at **182** by inserting **2**, **6**, **7** and **14** into the gaps on each line?

- (◯×◯+◯)×◯ = 182 (2 different ways!)
- (◯+◯)×◯×half◯ = 182

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

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