**The Main Challenge**

Following on from ** DAY 240**, here’s another one of the unique *Keith Number* challenges made famous by **Mike Keith** and similar to the *Fibonacci* sequence. If you like playing around with numbers, you’ll love having a go at this fun concept.

The 1st 2-digit *Keith Number*, **14**, is worked out by following a pattern:

- 1 4 5 9
**14**

1+4=5; 4+5=9; 5+9=**14** (the total arrives back to the original number).

The 2nd 2-digit *Keith Number*, **19**, is worked out in a similar way:

- 1 9 10
**19**

1+9=10; 9+10=**19** (the total again arrives back to the original number).

By following this pattern, the 3rd and 4th 2-digit *Keith Numbers* are **28** and **47**:

- 2 8 10 18
**28** - 4 7 11 18 29
**47**

Can you continue this process and locate the only other two *Keith Numbers* **below 100**?

**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 & 3rd rows contain the following fourteen numbers:

8 13 17 25 28 36 42 45 48 55 63 64 66 80

What is the sum of the square numbers?

**T****he Factors Challenge**

**The Mathematically Possible Challenge**

Using **8**, **10** and **12 **once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

1 4 9 16 25 36 49 64 81 100

#*SquareNumbers*

**The Target**** ****Challenge**

Can you arrive at **292** by inserting **2**, **3**, **4**, **5** and **6** into the gaps below?

- ◯×(◯³×◯²+(◯–◯)²) = 292

**Answers **can be found **here**.

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