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

Read the following ten clues about a particular number:

- it’s less than 100,
- it’s one more than a multiple of 3,
- exactly one of its two digits is prime,
- you get a prime if you reverse its digits,
- it’s not a multiple of 5,
- it’s not a prime number,
- it has exactly four factors,
- it’s not a square number,
- the sum of its digits is prime,
- if you multiply it by 5, the answer is greater than 100.

Can you find the mystery number?

**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 & 3rd rows contain the following fourteen numbers:

2 9 13 14 15 22 25 36 40 42 45 66 72 80

How many multiples of 12 are on the list?

**The 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 SIX ways of making **99 **when using *Lagrange’s Theorem*. Can you find them all?

**The Mathematically Possible Challenge**

Using **5**, **7** and **10 **once each, with + – × ÷ available, which TWO numbers it is possible to make from the list below?

12 24 36 48 60 72 84 96 108 120

#*12TimesTable*

**The Target Challenge**

Can you arrive at **99** by inserting **2**, **3**, **5** and **9** into the gaps on each line?

- (◯×◯+◯)×◯ = 99
- ◯×◯×◯+◯² = 99
- (◯+◯)²+◯–◯² = 99
- ◯²×◯²–◯²÷◯ = 99

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

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