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

Today’s task is to multiply two numbers together, then either add or subtract the third number to achieve the target answer of **37**.

Using the formula **(a×b)±c**, where a, b and c are three unique digits from **1-9**, one way of achieving 37 is (7×5)+2; can you find the other SEVEN ways?

[Note: (7×5)+2 = 37 and (5×7)+2 = 37 counts as just ONE way.]

**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 5th & 6th rows of the playing board contain the following fourteen numbers:

5 6 7 12 16 18 20 21 33 49 50 56 81 84

From the list, which three different numbers have a sum of 100?

**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 is only ONE way to make **224 **when using *Lagrange’s Theorem*. Can you find it?

**The Mathematically Possible Challenge**

Using **4**, **6** and **9 **once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

13 26 39 52 65 78 91 104 117 130

#*13TimesTable*

**The Target Challenge**

Can you arrive at **224** by inserting **1**, **2**, **7** and **7** into the gaps on each line?

- ◯×◯²×(◯+◯) = 224
- ◯⁵×◯³×◯²÷◯ = 224

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

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