**The Main Challenge**

This is similar in style to the challenges found at our popular **Mathelona** number puzzle pocket book. Click the link for more details.

◯ + ◯ = ◯

◯ + ◯ = ◯

◯ + ◯ = ◯

Can you insert 0, 0, 1, 1, 2, 3, 3, 4 and 4 into the nine gaps above so that all three lines work out arithmetically?

**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 4th & 5th rows of the playing board contain the following fourteen numbers:

3 6 7 10 16 21 32 35 44 50 54 60 81 84

List THREE sets of three different numbers, each having a sum of 77.

**T****he 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).

Show how you can make **194**, in TEN 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 FOUR numbers is it possible to make from the list below?

1 4 9 16 25 36 49 64 81 100

#*SquareNumbers*

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

Can you arrive at **194** by inserting **6**, **8**, **10** and **12** into the gaps on each line?

- (◯+◯)×◯–◯ = 194
- double(◯×◯)+√(◯–◯) = 194

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

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