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

Using each of the numbers **0.5**, **1**, **1.5** and **2** once each, with the four arithmetical operations + – × ÷ available, can you arrive at the target answer of **7**?

For the number puzzle enthusiast, can you find a 2nd way of making **7**?

**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 2nd & 5th rows contain the following fourteen numbers:

6 7 8 16 17 21 28 48 50 55 63 64 81 84

Which THREE numbers, when 19 is added to each of them, become square numbers?

**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 FIVE ways of making **101 **when using *Lagrange’s Theorem*. Can you find them all?

**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?

1 4 9 16 25 36 49 64 81 100

#*SquareNumbers*

**The Target Challenge**

Can you arrive at **101** by inserting **5**, **8**, **10** and **11** into the gaps on each line?

- ◯×◯–(◯–◯)² = 101
- (◯+◯)×◯+◯ = 101
- ◯×◯+◯+double◯ = 101

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

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