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

Starting from **ONE**, what is the 7th whole number, when written in English, that does NOT contain the letter ‘E’?

**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 & 3rd rows contain the following fourteen numbers:

2 9 13 14 15 22 25 36 40 42 45 66 72 80

List THREE sets of four different numbers that all have a sum of 200, and THREE 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 SEVEN ways of making **100 **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?

2 3 5 7 11 13 17 19 23 29

#*PrimeNumbers*

**The Target Challenge**

Can you arrive at **100** by inserting **4**, **5**, **8** and **10** into the gaps on each line?

- ◯×◯+◯×◯ = 100
- (◯+◯÷√◯)×◯ = 100
- ◯²×(◯+◯–◯) = 100
- (◯³÷◯)×◯÷◯ = 100
- ◯²×(◯+◯–◯)² = 100
- (◯×◯+◯)×√◯ = 100
- ((◯×◯)÷(◯–◯))² = 100

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

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