**Th**** e Main Challenge**

If you added together the first seven odd numbers that do not contain a **3**, **5** or **7** as part of their number or are not multiples of **3**, **5** or **7**, what is your answer?

**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 & 3rd rows of the playing board contain the following fourteen numbers:

2 9 13 14 15 22 25 36 40 42 45 66 72 80

What is the average of the three consecutive numbers listed above?

**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 THIRTEEN different ways to make **202 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

Using **5**, **7** and **11 **once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

7 14 21 28 35 42 49 56 63 70

#*7TimesTable*

**The Target ****Challeng****e**

Can you arrive at **202** by inserting **7**, **8**, **13** and **14** into the gaps on each line?

- ◯×◯+◯×◯ = 202
- ◯²+(◯–◯)²–double◯ = 202

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

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