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

A young mathematician originally from Nigeria called Chika, who now lives in London, has come up with a brilliant way of testing whether a number is divisible by 7.

Multiply the unit digit by 5. Keep the answer to one side! Treat the rest of the digits as a separate number and add it to your stored number. If this sum is divisible by 7, your original number is a multiple of 7, easy!!

If the sum is itself a big number, you can repeat the process with this new number.

For example, we shall test this theory by using **406**:

- Multiply the unit number (
**6**) by 5, which gives us 30, - The rest of the number (
**40**) is added to 30 (from above), giving us**70**, - Is 70 a multiple of 7? YES, therefore
**406 is a multiple of 7**.

Using the above algorithm, which TWO of the following are NOT multiples of 7?

245 308 476 557 693 735 811 994

**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 rows of the playing board contain the following fourteen numbers:

5 12 13 18 20 25 33 36 42 45 49 56 66 80

What is the difference between the totals of the odd numbers and even numbers?

**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 ELEVEN different ways to make **237 **when using *Lagrange’s Theorem*. How many of them can you find?

**The Mathematically Possible Challenge**

Using **2**, **5** and **10 **once each, with + – × ÷ available, which are the only THREE numbers 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 **237** by inserting **1**, **2**, **3**, **4** and **5** into the gaps below?

- (◯+◯)²×(◯+◯)–double◯ = 237

**A****nswers **can be found **here**.

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