**T**** he Main Challenge**

You’ve rolled the numbers **2**, **3** and **4** with three dice. Using these once each, with + – × ÷ available, what is the lowest positive whole number it is NOT possible to make?

**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 & 4th rows contain the following fourteen numbers:

2 3 9 10 14 15 22 32 35 40 44 54 60 72

Which three different numbers have a sum of 100?

**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 **36 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **6** and **11 **once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

1 4 9 16 25 36 49 64 81 100

#*SquareNumbers*

**The Target Challenge**

Can you arrive at **36** by inserting **2**, **3**, **4** and **6** into the gaps on each line?

- (◯+◯+◯)×◯ = 36
- (◯²+◯)×◯÷◯ = 36
- (◯–◯)×◯×◯ = 36
- ◯²×(◯+◯–◯) = 36 (2 different ways)

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

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