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

Read the following facts below about a particular number:

- It is a 2-digit number,
- It is an even number,
- When the two digits are added together they make another 2-digit even number that is also a square number.

What is the number?

**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 sum of the multiples of 11 and the sum of the multiples of 10?

**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 SIX ways of making **121 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **4** and **12 **once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

9 18 27 36 45 54 63 72 81 90

#*9TimesTable*

**The Target Challenge**

Can you arrive at **12**1 by inserting **4**, **5**, **6** and **7** into the gaps on each line?

- (◯+◯)×(◯+◯) = 121
- (◯+◯)²×(◯–◯) = 121
- ◯³–◯×(◯–◯) = 121

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

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