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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?

Bracelets

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

Sweets in a Box

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Swimming Pool

Age 5 to 11 Challenge Level:

We had five solutions sent in altogether. Joe from St. Anne's school sent in a full solution as follows:

1. 7 steps
2. 8 steps
3. 9 steps
4. light green -1
purple -2
red -3
yellow -4
dark green -5
blue -6

Pranesh from Holy Garden school also sent in correct answers for the three questions. We had a pleasant chatty note sent in by Charlie from Culford Prep School as follows:


For all the coloured steps, give them the numbers -1, -2, and so on. The unnumbered non-coloured step could be 0 so now you could have the numbers going down in face value. If this is not true, sorry for wasting your time, but in my eyes it worked fine, thank you for taking your time to read this.

You are absolutely right in your thinking, well done!

The following solution also came in but unfortunately no name or school was attached.


Solution1

Finally, from Hotwells School:


Solution2