**The Main Challenge**

Three people answered four multiple choice problems each, with a choice of A B or C, and their responses are shown here:

- Tim: A B B C
- Tam: A C B A
- Tom: B B C A

If two people answered two questions correctly and one person had them all wrong, can you work out what the correct answers could be?

**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 3rd & 5th rows contain the following fourteen numbers:

6 7 13 16 21 25 36 42 45 50 66 80 81 84

Which of the square numbers listed has the most number of factors?

**The 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 **175**, in EIGHT different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **4**, **6** and **10** once each, with + – × ÷ available, which THREE target numbers is it possible to make from the list below?

1 3 5 7 9 11 13 15 17 19

#*OddNumber*s

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

Can you arrive at **175** by inserting **1**, **5**, **10** and **15** into the gaps on each line?

- ◯²+(◯×◯×◯) = 175
- ◯²–(◯×◯×◯) = 175
- (◯+◯)×◯+double◯ = 175
- (◯+◯)×◯+treble◯ = 175

**Answers **can be found **here**.

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