**The Main Challenge**

You have the same starting number and final answer, both **32**, with lots of arithmetical steps in between, but the 10th step is missing! What should it be if it involves an integer?

Start with the number **32**, then:

–5 ÷9 +4 ×3 –3 ÷2 ×5 –5 ÷2 **?** ×2 +4 ÷3 ×2 = **32**

For the real number puzzle enthusiast, there is another possible step which involves multiplying by a decimal number. What is it?

**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 columns contain the following fourteen numbers:

5 9 13 21 22 24 27 28 32 50 55 56 60 66

Which multiple of 7, when adding 1 to it, becomes a prime number?

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

**The Mathematically Possible Challenge**

Using **5**, **6** and **12 **once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

4 8 12 16 20 24 28 32 36 40

#*4TimesTable*

**The Target Challenge**

Can you arrive at **322** by inserting **6**, **7**, **8**, **9** and **10** into the gaps below?

- (◯²×(◯–◯)+◯)×◯ = 322

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

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