**T**** he Main Challenge**

Each of the five numbers below is the product of two prime numbers:

15 35 77 143 323

Which is the odd one out, and why?

**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 5th & 6th rows of the playing board contain the following fourteen numbers:

5 6 7 12 16 18 20 21 33 49 50 56 81 84

What is the sum of the multiples of 7?

**T****he 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 FOURTEEN different ways to make **225 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

Using **4**, **6** and **9 **once each, with + – × ÷ available, which are the FOUR numbers it is possible to make from the list below?

15 30 45 60 75 90 105 120 135 150

#*15TimesTable*

**The Target Challenge**

Can you arrive at **225** by inserting **3**, **4**, **5** and **9** into the gaps on each line?

- (◯–◯)×◯×◯² = 225 (there are 2 ways!)
- (◯+◯+◯–◯)² = 225

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

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