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

Which is the ONLY way to make **38** when adding together SIX unique digits from **1-9**?

**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 4th & 5th rows contain the following fourteen numbers:

3 6 7 10 16 21 32 35 44 50 54 60 81 84

Which number, when 5 is added to it, becomes a square number?

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

**The Mathematically Possible Challenge**

Using **2**, **3** 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 **87** by inserting **3**, **4**, **6** and **7** into the gaps on each line?

- ◯×◯×√◯+◯ = 87
- ◯²×(◯+◯)–double◯ = 87
- (◯+◯)²+double(◯–◯) = 87

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

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