**T**** he Main Challenge**

Read the following facts:

- I am a 2-digit number,
- both my digits are odd,
- the sum of both digits is less than 10,
- my 1st digit is smaller than my 2nd digit, and
- I am a multiple of 3.

Which number am I?

**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

From the list, what is the sum of the multiples of 10?

**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 **219 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

Using **4**, **6** and **9 **once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

12 24 36 48 60 72 84 96 108 120

#*12TimesTable*

**The Target Challenge**

Can you arrive at **219** by inserting **3**, **4**, **9** and **16** into the gaps on each line?

- (◯×◯+◯)×◯ = 219
- ◯²×◯–(◯+double◯) = 219

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

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