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

Using all four decimal numbers **0.4**, **0.8**, **1.2** and **3.5** once each, and with + – × ÷ available, can you arrive at the target answer of **7**?

**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 2nd & 4th rows contain the following fourteen numbers:

3 8 10 17 28 32 35 44 48 54 55 60 63 64

What is the difference between the two prime numbers 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 **128 **when using *Lagrange’s Theorem*. Can you find it?

**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?

3 6 9 12 15 18 21 24 27 30

#*3TimesTable*

**The Target Challenge**

Can you arrive at **128** by inserting **4**, **8**, **10** and **12** into the gaps on each line?

- ◯×◯+◯×◯ = 128
- ◯×◯+◯²–◯ = 128
- ◯⁴×◯÷(◯+◯) = 128

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

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