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

Find the sum of the following three numbers:

- twelve thousand and two
- thirty five thousand and thirty-five
- fifty five thousand, one hundred and fifty-five

Write your answer in words.

**The**** 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 2nd & 3rd rows contain the following fourteen numbers:

8 13 17 25 28 36 42 45 48 55 63 64 66 80

How many multiples of 9 are on the list?

**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 **85 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **3** and **11 **once each, with + – × ÷ available, which is the ONLY number that 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 **85** by inserting **5**, **10**, **15** and **20** into the gaps on each line?

- ◯×◯+◯–◯ = 85
- ◯²+◯×(◯÷◯)² = 85
- (◯+◯÷◯)×◯ = 85

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

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