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

From all the odd numbers in the range **1-23** inclusive, eliminate all prime numbers and multiples of 3. Which is the only number that remains?

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

3 10 13 25 32 35 36 42 44 45 54 60 66 80

Which number, when 10 is added to it, becomes a square number?

**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 ELEVEN different ways to make **218 **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 only TWO numbers it is possible to make from the list below?

11 22 33 44 55 66 77 88 99 110

#*11TimesTable*

**The Target Challenge**

Can you arrive at **218** by inserting **4**, **10**, **12** and **17** into the gaps on each line?

- ◯×◯+◯+◯ = 218
- ◯×◯+◯×◯ = 218
- ◯²–◯×(◯–◯)+1 = 218
- ◯×(◯+◯)+treble◯–1 = 218

**A****nswers **can be found **here**.

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