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

Try the following challenge from my number puzzle pocket book. Further details can be found by clicking on **Mathelona**.

Your task is to make all three lines work out arithmetically by correctly placing the 12 digits **0 0 1 1 2 2 3 3 4 4 6 **and** 6 **into the 12 gaps below. Can you do it?

◯ + ◯ = 4 = ◯ – ◯

◯ + ◯ = 6 = ◯ × ◯

◯ + ◯ = 3 = ◯ ÷ ◯

**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 5th & 6th rows of the playing board contain the following fourteen numbers:

5 6 7 12 16 18 20 21 33 49 50 56 81 84

What is the answer when the larger multiple of 10 is divided by the smaller one?

**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).

There are NINE different ways to make **223 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

Using **4**, **6** and **9 **once each, with + – × ÷ available, which are the FIVE numbers it is possible to make from the list below?

1 3 5 7 9 11 13 15 17 19

#*OddNumbers*

**The Target Challenge**

Can you arrive at **223** by inserting **3**, **7**, **8** and **20** into the gaps on each line?

- ◯²×◯+◯×◯ = 223
- (◯⁵–◯)÷(◯–◯) = 223

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

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