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

Find the answer to this large number trail which involves fourteen arithmetical steps and includes fraction and percentage calculations.

Start with the number **11**, then:

- double it
- 50% of this
- +50
- subtract thirty-five
- ÷2
- +37
- 3/5 of this
- +70
- –2%
- 1/2 of this
- +311
- subtract twenty
- add ten
- ÷7

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 1st & 7th rows contain the following fourteen numbers:

2 4 9 11 14 15 22 24 27 30 40 70 72 77

What is the difference between the highest multiples of 5 and 6?

**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 only TWO ways of making **17 **when using *Lagrange’s Theorem*. Can you find both?

**The Mathematically Possible Challenge**

Using **5**, **6** and **8 **once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

7 14 21 28 35 42 49 56 63 70

#*7TimesTable*

**The Target Challenge**

Can you arrive at **17** by inserting **2**, **5**, **6** and **6** into the gaps on each line?

- ◯²–√(◯×◯)–◯ = 17
- ◯²×◯÷◯+◯ = 17
- (◯÷◯+◯)×◯ = 17

**A****nswers **can be found **here**.

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