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

Study the seven clues below and place the numbers **1-9** into the nine positions. Each number should appear exactly once:

**x x x**

**x x x**

**x x x**

Clues:

- The 8 is directly right of the 9,
- The 9 is directly above the 6,
- The 6 is directly right of the 4,
- The 4 is higher than the 1,
- The 1 is further right of the 3,
- The 3 is lower than the 7,
- The 7 is directly above the 5.

**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

What is the biggest difference between two consecutive numbers on the above 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 NINE different ways to make **206 **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 that is possible to make from the list below?

11 22 33 44 55 66 77 88 99 110

#*11TimesTable*

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

Can you arrive at **206** by inserting **10**, **12**, **14 **and **18** into the gaps on each line?

- ◯×◯+◯+◯ = 206
- ◯×◯+◯+double◯ = 206

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

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