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

Three UNIQUE digits from **1-9** must be used to arrive at a specified target number by multiplying two numbers together and either adding or subtracting the third number.

Today, your goal is to make **19**. The three numbers in each calculation must be different.

One way to make **19** is (7×2)+5, can you find the other THIRTEEN ways?

[Note: (7×2)+5 = 19 and (2×7)+5 = 19 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 3rd & 6th rows of the playing board contain the following fourteen numbers:

5 12 13 18 20 25 33 36 42 45 49 56 66 80

What is the sum of the multiples of 5 listed above?

**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 SIX different ways to make **239 **when using *Lagrange’s Theorem*. How many of them can you find?

**The Mathematically Possible Challenge**

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

6 12 18 24 30 36 42 48 54 60

#*6TimesTable*

**The Target Challenge**

Can you arrive at **239** by inserting **1**, **2**, **3**, **5** and **6** into the gaps below?

- (◯+◯)²×◯–◯×◯ = 239

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

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