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

Starting from 1, find the sum of the first SEVEN whole numbers that do not contain a 3, 5 or 7 as part of their number, nor are multiples of 3, 5 or 7.

**T****he**** 7puzzle Challenge**

The playing board of **the 7puzzle game** is a 7-by-7 grid of 49 different numbers, ranging from **2 **up to **84**.

The 4th & 6th rows contain the following fourteen numbers:

3 5 10 12 18 20 32 33 35 44 49 54 56 60

What is the sum of the multiples 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 **58 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **1**, **6** and **7 **once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

5 10 15 20 25 30 35 40 45 50

#*5TimesTable*

**The Target Challenge**

Can you arrive at **58** by inserting **4**, **6**, **8** and **10** into the gaps on each line?

- ◯×◯–◯÷◯ = 58
- ◯²+◯+◯+◯ = 58
- ◯²–√(◯×(◯–◯)) = 58

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

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