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

The two sections below both contain eight letters, **A-H**. Each letter has an addition calculation attached, all involving 2-digit numbers.

Which is the only letter that has exactly the same answer in both sections?

- Section 1

D:68+18 B:51+14 E:47+31 H:62+32 A:44+29 G:59+25 C:36+23 F:38+26

- Section 2

E:64+28 A:31+27 F:34+22 B:43+19 G:48+36 C:54+16 D:48+21 H:50+38

**The**** 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 2nd & 7th rows contain the following fourteen numbers:

4 8 11 17 24 27 28 30 48 55 63 64 70 77

Which three different numbers have a total which is also present on the list?

**The Lagrange Challenge**

*Lagrange’s Four-Square Theorem* states that every 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).

Show how you can make **168**, in FOUR different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Using **4**, **6** and **10** once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

7 14 21 28 35 42 49 56 63 70

#*7TimesTable*

**The Target Challenge**

Can you arrive at **168** by inserting **2**, **4**, **6** and **9** into the gaps on each line?

- (◯–◯)×◯×◯ = 168
- ◯³×√◯–◯²×◯ = 168

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

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