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

You must try and make all three lines work out arithmetically by inserting the twelve digits **0 0 1 1 2 3 3 4 5 6 6 **and** 7** into the gaps:

◯ + ◯ = 7 = ◯ – ◯

◯ + ◯ = 5 = ◯ × ◯

◯ + ◯ = 6 = ◯ ÷ ◯

If you enjoy this, click **Mathelona** for further details of our unique number puzzles.

**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 & 6th rows contain the following fourteen numbers:

2 5 9 12 14 15 18 20 22 33 40 49 56 72

Which two numbers have a difference of 21?

**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 **177**, in EIGHT different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Using **3**, **6** and **12** once each, with + – × ÷ available, which FOUR target numbers is it possible to make from the list below?

5 10 15 20 25 30 35 40 45 50

#*5TimesTable*

**The Target Challeng****e**

Can you arrive at **177** by inserting **1**, **7**, **9** and **11** into the gaps on each line?

- ◯×(◯+◯)+◯ = 177
- ◯²+(◯–◯)×◯ = 177

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

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