** The Main Challenge**

. . . is a tricky **5puzzle**-style question that’s a real mouth-watering prospect for the number puzzle enthusiast.

Using the numbers **1**, **2**, **3**, **4** and **5** once each, with + – × ÷ available, it is possible to make the vast majority of numbers in the range **50-100**.

For example, to arrive at **50** and **51**, you could do:

- (4+3+2+1)×5 =
**50**, - (4×3–2)×5+1 =
**51**, and so on . . .

Continuing your calculations, what is the LOWEST number in this range that it’s NOT possible to make?

**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 columns contain the following fourteen numbers:

4 7 12 15 17 30 35 36 40 49 54 64 80 81

How many square numbers are listed above?

**T****he Factors Challenge**

**The Mathematically Possible Challenge**

Using **5**, **6** and **12 **once each, with + – × ÷ available, which are the only THREE numbers it is 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 **327** by inserting **3**, **5**, **5**, **7** and **7** into the gaps below?

- ((◯+◯)²–◯×◯)×◯ = 327

**Answers **can be found **here**.

**Click Paul Godding for details of online maths tuition.**