**The Main Challenge**

What is the sum of the first seven 2-digit even 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 3rd & 4th rows of the playing board contain the following fourteen numbers:

3 10 13 25 32 35 36 42 44 45 54 60 66 80

Which statement is true?

- There are
**more**multiples of 9 than multiples of 10 on the list - There are
**equal**numbers of multiples of 9 and multiples of 10 on the list - There are
**less**multiples of 9 than multiples of 10 on the list

**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 TEN different ways to make **217 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **4**, **6** and **9 **once each, with + – × ÷ available, which are the FOUR 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 **217** by inserting **3**, **7**, **11** and **14** into the gaps on each line?

- ◯×◯×◯–◯ = 217
- ◯×◯+◯²×◯ = 217
- ◯×(◯+◯+1)+◯ = 217
- ◯×(◯+◯–1)–◯ = 217

**Answers **can be found **here**.

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