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

Read the following clues to work out which number I am today:

- I am a 2-digit number,
- Both 3 and 4 divide exactly into me,
- My two digits add up to 9,
- I am not a square number.

Who am I?

**T****he**** 7puzzle Challenge**

The playing board of **the 7puzzle game** is a 7-by-7 grid of 49 different numbers, ranging from **2 **up to **84**.

The 4th & 7th rows contain the following fourteen numbers:

3 4 10 11 24 27 30 32 35 44 54 60 70 77

Which even number, when halved, becomes a square number?

**T****he Lagrange Challenge**

*Lagrange’s Four-Square Theorem* states that every 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).

Show how you can make **184**, in TWO different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Using **3**, **6** and **12** once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

1 4 9 16 25 36 49 64 81 100

#*SquareNumbers*

**The Target ****Challeng****e**

Can you arrive at **184** by inserting **4**, **5**, **6** and **8** into the gaps on each line?

- (◯×◯+◯)×◯ = 184
- (◯×◯+half◯)×◯ = 184

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

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