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

Can you place the 12 numbers **0 1 2 2 3 3 4 6 6 7 9** and **9** into the 12 gaps below so that all three lines work out arithmetically?

◯ + ◯ = 6 = ◯ – ◯

◯ + ◯ = 18 = ◯ × ◯

◯ + ◯ = 3 = ◯ ÷ ◯

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**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

How many triangular numbers are listed above?

**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 is only ONE way of making **56 **when using *Lagrange’s Theorem*. Can you find it?

**The Mathematically Possible Challenge**

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

3 6 9 12 15 18 21 24 27 30

#*3TimesTable*

**The Target Challenge**

Can you arrive at **56** by inserting **2**, **4**, **6** and **8** into the gaps on each line?

- ◯×◯+◯×◯ = 56
- ◯²+◯×◯+◯ = 56
- (◯+◯)×◯–◯ = 56
- (◯+◯)×◯–◯⁴ = 56
- ◯×(◯+◯÷◯) = 56
- (◯+◯)×(◯–◯)² = 56

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

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