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

Start with the number **50**, then:

+27 –42 divide by 5 ×4 +50% two-thirds of this ÷7 = **?**

What is your final answer to this 7-step number trail?

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

2 3 9 10 14 15 22 32 35 40 44 54 60 72

What is the difference between the highest odd number and lowest multiple of 11?

**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 FIVE ways of making **143 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using the three digits **2**, **6** and **9** once each, with + – × ÷ available, which are the SIX numbers it is possible to make from the list below?

6 12 18 24 30 36 42 48 54 60

#*6TimesTable*

**The Target Challenge**

Can you arrive at **143** by inserting **3**, **4**, **7** and **10** into the gaps on each line?

- (◯+◯)×(◯+◯) = 143
- ◯³–◯²×double(◯–◯) = 143

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

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