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

Using the numbers **3**, **5** and **5** once each, with + – × ÷ available, which FOUR numbers from the following list are NOT mathematically possible to make?

1 2 3 4 7 10 13 15 18 20 22 25 28 30

**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 6th & 7th rows contain the following fourteen numbers:

4 5 11 12 18 20 24 27 30 33 49 56 70 77

What is the difference between the two prime numbers 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 FOUR ways of making **94 **when using *Lagrange’s Theorem*. Can you find them?

**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?

7 14 21 28 35 42 49 56 63 70

#*7TimesTable*

**The Target Challenge**

Can you arrive at **94** by inserting **3**, **5**, **7** and **10** into the gaps on each line?

- ◯³–◯×◯–◯= 94
- ◯²–◯×(◯–◯) = 94
- ◯²+◯×(◯+◯)= 94 (2 different ways)

**A****nswers **can be found **here**.