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

Your starting number is **18** and your task is to arrive at the same final answer. There are ten arithmetical steps from beginning to end, each one involving a whole number, but the 9th (and penultimate) step is missing! What must it be?

÷2 +3 –8 ×6 +4 –3 ÷5 ×2 **?** ×2 = **18**

**T****he**** 7puzzle Challenge**

The playing board of **the 7puzzle game** is a 7-by-7 grid of 49 different numbers, ranging from **2 **up to **84**.

The 4th & 6th rows contain the following fourteen numbers:

3 5 10 12 18 20 32 33 35 44 49 54 56 60

What is the difference between the lowest and highest multiples of 4?

**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 THREE ways of making **59 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **1**, **6** and **7 **once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

6 12 18 24 30 36 42 48 54 60

#*6TimesTable*

**The Target Challenge**

Can you arrive at **59** by inserting **4**, **5**, **6** and **10** into the gaps on each line?

- ◯×◯+◯–◯ = 59
- ◯²+◯×◯+◯ = 59
- (◯+◯)×◯–◯ = 59

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

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