### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

### It Figures

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

### Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

# Flashing Lights

##### Stage: 2 Challenge Level:

(Thank you to Norrie McKay and the lights over Tokyo Bay for this problem)

There were many correct answers sent in for this problem. As Primary Maths Club (International School of Toulouse) pointed out, it helps if you start counting seconds from the first time the two lights flashed together (at zero seconds).

Some people thought about a number line, others looked for a number that both of the numbers of seconds (4 and 5) would divide into (common multiple). Here are two very well explained solutions.

Holly, Harriette, Caroline, Florence and Rebecca from The Mount School, York:

1st light 0 - 4 - 8 - 12 - 16 - 20 - 24 - ......
2nd light 0 - 5 - 10 - 15 - 20 - 25 - ........

They flash at the same time every 20 seconds 0 - 20 - 40 - 60
That's four times in all.

For two lights the pattern was every 20 seconds and 4 x 5 = 20
For the three lights it is going to be 4 x 5 x 7 = 140 seconds or 2 minutes 20 seconds

Christina from Marlborough Primary School :

To work this out you need to find a multiple of both 5 and 4 which is 20. So the lights flash together every 20 seconds and to find out how many times they flash in one minute you need to do 60/20 = 3 which means that they flash together 3 times a minute.

You need to find a multiple of 20 and seven to work out how many minutes before all of the lights flash together. 20 x 7 = 140 sec = 2 mins 20 sec

Well done to all of the following people: Jesse, Edward, Daniel and Thomas from Tattingstone School who did some very good work with finding the multiples. Lily from Sotogrande International School, Daniel from Anglo-Chinese School, Singapore, Abigail, Charles and David from Moorgate Primary School, Staffordshire, Jason from Priory School, Thomas from St Francis School, Maldon and Ashley.