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

To solve this *Octaplus* puzzle, find the values of eight letters, **A to H**, from the given clues. Each letter contains a different whole number in the range **1-50**:

- B minus E is either 14 or 15,
- C is one-quarter of B,
- F is one-seventh of E,
- D is half of B,
- G is H plus C,
- one-third of E is an odd number,
- H is one-third of D,
- A is 150 minus the sum of the other seven 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 2nd & 4th rows contain the following fourteen numbers:

3 8 10 17 28 32 35 44 48 54 55 60 63 64

How many square numbers are listed?

**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 is only ONE way of making **23 **when using *Lagrange’s Theorem*. Can you find it?

**The Mathematically Possible Challenge**

Using **5**, **6** and **8 **once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

30 31 32 33 34 35 36 37 38 39

#*NumbersIn30s*

**The Target Challenge**

Can you arrive at **23** by inserting **2**, **3**, **4** and **6** into the gaps on each line?

- ◯×◯+◯–◯ = 23
- (◯³–◯×◯)÷◯ = 23
- (◯²+◯)–(◯³+◯²) = 23

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

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