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

Here’s a number trail involving 16 arithmetical steps. Start with the number **2**, then:

- +33
- divide by seven
- ×3
- add ten percent
- double this
- add three
- find the square root of this
- +7
- 1/2 of this
- add nineteen point five
- subtract two
- ÷6
- +15
- ×5
- –93
- ÷2

What is your final answer?

**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 3rd & 6th rows contain the following fourteen numbers:

5 12 13 18 20 25 33 36 42 45 49 56 66 80

Which two numbers, when doubled, are also present on the list?

**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 **135 **when using *Lagrange’s Theorem*. Can you find them?

**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?

10 20 30 40 50 60 70 80 90 100

#*10TimesTable*

**The Target Challenge**

Can you arrive at **135** by inserting **4**, **5**, **9** and **12** into the gaps on each line?

- ◯²–◯×(◯–◯) = 135
- ◯×◯×◯÷◯ = 135
- (◯+◯)²+half(◯×◯) = 135

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

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