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

Only one of the following 3-digit numbers is **divisible by 3**. Which one?

136 139 245 248 353 357 466 469 572 578 680

[Note: If you don’t know the trick on how to work this out, please get in touch.]

**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 rows contain the following fourteen numbers:

2 4 9 11 14 15 22 24 27 30 40 70 72 77

What is the sum of the multiples of 7?

**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 TWO ways of making **19 **when using *Lagrange’s Theorem*. Can you find both?

**The Mathematically Possible Challenge**

Using **5**, **6** and **8 **once each, with + – × ÷ available, which are the only TWO 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 **19** by inserting **1**, **2**, **3** and **4** into the gaps on each line?

- (◯+◯)×◯+◯ = 19
- (◯+◯)×◯–◯ = 19
- ◯²+(◯+◯)×◯ = 19

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

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