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

The following clues are given to help you find a particular number:

- I am a 2-digit number
- my two digits have a difference of one
- I am a multiple of 7
- the number immediately below me is a prime number

Who am I?

**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 1st & 4th rows of the playing board contain the following fourteen numbers:

2 3 9 10 14 15 22 32 35 40 44 54 60 72

How many multiples of 4 are listed?

**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 SEVENTEEN different ways to make **250 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

Using **5**, **8** and **11 **once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

4 8 12 16 20 24 28 32 36 40

#*4TimesTable*

**The Target**** Challenge**

Can you arrive at **250** by inserting **5**, **10**, **15**, **20** and **25** into the gaps below?

- ◯×◯–(◯²+◯+◯) = 250

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

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