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

This describes a particular number **less than 100**:

- its digits add up to
**12**, - if the unit digit is subtracted from the tens digit, then doubled, the answer is also
**12**.

What is the number?

**T****he**** 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 contain the following fourteen numbers:

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

List THREE different numbers that have a sum of 77.

**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 FIVE ways of making **111 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **1**, **4** and **9 **once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

9 18 27 36 45 54 63 72 81 90

#*9TimesTable*

**The Target Challenge**

Can you arrive at **111** by inserting **2**, **3**, **5** and **7** into the gaps on both lines?

- (◯×◯+◯)×◯ = 111
- (◯+◯)²+double(◯×◯) = 111

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

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