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

Can you place the 12 numbers **1 1 2 2 3 3 4 4 5 6 7** and **8** into the 12 gaps below so that all four equations work out arithmetically?

◯ + ◯ = ◯

◯ + ◯ = ◯

◯ + ◯ = ◯

◯ + ◯ = ◯

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

3 8 10 17 28 32 35 44 48 54 55 60 63 64

What is the difference between the sum of the multiples of 8 and the sum of the multiples of 7?

**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 TEN ways of making **130 **when using *Lagrange’s Theorem*. Can you find them all?

**The Mathematically Possible Challenge**

Using **3**, **6** and **10 **once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

5 10 15 20 25 30 35 40 45 50

#*5TimesTable*

**The Target Challenge**

Can you arrive at **130** by inserting **2**, **3**, **5** and **10** into the gaps on each line?

- (◯+◯)×◯×◯ = 130
- (◯×◯–◯)×◯ = 130
- ◯²+◯²+◯²–◯² = 130

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

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