**The Main Challenge**

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

**x x x**

**x x x**

**x x x**

Clues:

- The 6 is higher than the 7, but lower than the 3,
- The 3 is further right than the 9,
- The 9 is directly above the 2,
- The 2 is directly right of the 5,
- The 5 is higher than the 1,
- The 1 is directly left of the 4,
- The 4 is further right than the 7.

**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 & 6th rows of the playing board contain the following fourteen numbers:

5 12 13 18 20 25 33 36 42 45 49 56 66 80

What is the sum of the multiples of 6?

**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 SIX different ways to make **236 **when using *Lagrange’s Theorem*. How many of them can you find?

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **2**, **5** and **10 **once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

3 6 9 12 15 18 21 24 27 30

#*3TimesTable*

**The Target Challenge**

Can you arrive at **236** in two different ways when inserting **1**, **2**, **3**, **4** and **5** into the gaps below?

- (◯+◯)³+◯×(◯+◯) = 236

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

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