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## 'Tea Cups' printed from http://nrich.maths.org/

Sophie from Bridge Learning Campus,
Bristol sent in the following, which pleased me in the way that she
describes her work.

1. I did the teacups first, white teacups first going down
diagonally, top left to bottom right, green tea cups next going
diagonally down from the top right to bottom left. It didn't matter
which one I did first.

2. I did the red teacups in the places I could put them and
added the blue teacups to the empty spaces.

3. Next I did the saucers on the top row to match the cup and
saucer, I did the column going downwards on the left and repeated
it on the other columns until I found the pattern.

4. I looked at the shapes with my teacher and by joining the
blue cups, I started to see a parallelogram in the blue cups and
one the same in the red teacups.

5. I changed teacups and saucers for numbers and saw that there
were patterns in the numbers, when I drew shapes over the same
numbers for the saucers, I saw four triangle like shapes with the
points going into the four corners. I enjoyed the
investigation!

More than half of the solutions had a common
slip-up in that there were several combinations of cups and saucers
that were repeated. The challenge is to have them mixed up so that
no two cup/saucers werre the same. I was very pleased to see that
various computer programs were being used to send in the solutions,
like Samuel, Minc and Julian from Manilla who sent this in:

However I've put all the solutions into the
same format for easy comparison. Well done! All of you listed
here: