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?
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?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
This was a tricky problem but we
received some detailed solutions - well done.
Frank, Noah and Ben from Stanford Junior
Sean, Ben, Lane and Jonathan from
Meridian Primary School told us about some of the things they
Pranjal from Garden International
School, Kuala Lumpur took these ideas a bit further and
Jong Woong, Jayme, Denise and Mariana,
also from Garden International School, have reasoned through this
problem very carefully. They told us how they worked to solve the
problem. First, they said they wrote down all the pairs possible
using the $4$, $5$, $6$, $7$, $8$, $10$, $11$ and $12$
Then they tried random cogs to see if
they worked and tried to find a pattern among them.
They asked themselves questions:
They then wrote:
Well done to all of you who sent a solution to
this problem. I wonder whether anyone else can find a way to
explain why cogs will only work if they have a HCF of $1$?