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

There are two sets of three consecutive numbers, in ascending order, whose sum is **less than** **50** and follow this sequence:

- triangular number – square number – prime number

Can you list both sets of numbers?

**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 difference between the totals of the odd numbers and even 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 ELEVEN different ways to make **237 **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?

4 8 12 16 20 24 28 32 36 40

#*4TimesTable*

**The Target Challenge**

Can you arrive at **237** by inserting **1**, **2**, **3**, **4** and **5** into the gaps below?

- (◯+◯)²×(◯+◯)–double◯ = 237

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

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