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

When listing the first SEVEN 3-digit numbers that do not contain a **0**, **1** or **2** as part of their number, what is the total of these listed numbers?

**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 2nd & 5th rows of the playing board contain the following fourteen numbers:

6 7 8 16 17 21 28 48 50 55 63 64 81 84

Which two numbers, when doubled, become square 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 NINE different ways to make **207 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

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

12 24 36 48 60 72 84 96 108 120

#*12TimesTable*

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

Can you arrive at **207** by inserting **3**, **9**, **10 **and **11** into the gaps on each line?

- (◯×◯–◯)×◯ = 207
- (◯²–◯–double◯)×◯ = 207

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

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