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

The seven musical letters, **A-G**, in the three sections below each contain an addition calculation. Only one letter has the same answer in all three sections, which one?

- Section 1

E: 11+6 G: 7+7 C: 10+4 A: 13+6 B: 9+4 F: 8+8 D: 9+3

- Section 2

A: 11+5 C: 13+5 F: 9+6 E: 15+3 D: 6+6 B: 8+5 G: 7+6

- Section 3

C: 11+3 B: 11+2 D: 7+4 G: 14+1 F: 12+3 E: 14+3 A: 15+4

**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 1st & 4th rows of the playing board contain the following fourteen numbers:

2 3 9 10 14 15 22 32 35 40 44 54 60 72

Which two separate numbers, when 9 is added to them, both become square numbers?

**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 FOURTEEN different ways to make **246 **when using *Lagrange’s Theorem*. How many can you find?

**The Mathematically Possible Challenge**

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

1 4 9 16 25 36 49 64 81 100

#*SquareNumbers*

**The Target**** Challenge**

Can you arrive at **246** by inserting **3**, **4**, **5**, **6** and **7** into the gaps below?

- (◯×◯+◯×◯)×◯ = 246

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

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