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

What is the total of all the square numbers from **1-100** inclusive?

**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

List FIVE sets of three different numbers that all 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 FIVE ways of making **91 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **5**, **7** and **10 **once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

4 8 12 16 20 24 28 32 36 40

#*4TimesTable*

**The Target Challenge**

Can you arrive at **91** by inserting **2**, **4**, **5** and **9** into the gaps on each line?

- (◯+◯)×(◯+◯) = 91
- ◯³+◯×(◯–◯) = 91
- ◯²×◯×√◯–◯ = 91

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

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