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

Solve this *Octaplus* puzzle by finding the values of the eight letters, **A to H**, from the given clues. Each letter contains a different whole number in the range **1-32**:

- D minus B is an even number,
- a third of D is an even number,
- G minus B is either 16 or 17,
- C is half of G, and E is half of C
- H is a third of B,
- D is equal to C plus H,
- F is either 18 or 20,
- A is 120 minus the sum of the other seven numbers.

**T****he**** 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 1st & 5th rows contain the following fourteen numbers:

2 6 7 9 14 15 16 21 22 40 50 72 81 84

Which three different numbers from the list have a sum of 77?

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

**The Mathematically Possible Challenge**

Using **8**, **9** and **10 **once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

80 81 82 83 84 85 86 87 88 89

#*NumbersIn80s*

**The Target Challenge**

Can you arrive at **54** by inserting **2**, **5**, **8** and **12** into the gaps on each line?

- ◯×◯+◯+◯ = 54
- ◯×◯+◯–◯ = 54
- (◯–◯)×◯–◯ = 54
- (³√◯+◯÷◯)×◯ = 54

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

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