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Well done all of you who sent in these
solutions. I am very pleased with the ways that you went about
doing this challenge and the different ways you showed your
Pupils from Chesterbrook Academy sent in
We first started off by doing column by column and row by row.
After we found out it would take us forever, we tried putting the
doubles (green green, blue blue, etc.) in the middle four squares.
This idea was given to us by our teacher, Mrs. Johnson. After that,
we built off the center.
Our answers were:
g r b w
b g w r
w b r g
g b r w
b w g r
r w g b
r g w b
w r b g
Then someone else from the same school
We figured it out by putting the doubles (white,white, green,green
Etc.) in the middle. Then we put the ones that were opposites
together and took each column too see if the patterns could go
there. If it didn't work we switched the middle until we finally
Here's Emma's Solution that she sent in in a
Andy sent in the following. I liked his method
for finding a solution by starting with the special diagonal and
then filling in. I've not come across this method before. This
solution has the added attraction (perhaps difficulty) that the
diagonals also have to obey the rule!
The answer is
BB WR GW RG
RW GG WB BR
WG BW RR GB
GR RB BG WW
B stands for blue
G stands for green
R stands for red
W stands for white
The first letter of each double is the saucer
The second letter of each double is the cup
First we have to put the cups and saucers that are the same colour
in a diagonal line. Then we work out the rest of the space by using
Eg BB GG
The space between BB and GG will be filled with RW and the opposite
space would be filled with WR. In the end all the space would be
filled in the the shape of a square and that is the answer.
Susie sent in these comments accompanied by
the Spreadsheet. This is the first time, out of hundreds of times,
that I've been presented with this method of finding a
solution.Well done Susie, (from Cathedral School, I wonder which
I made a 4 by 4 square and wrote in each square pairs of letters
AA, AB, AC to mean the colours of cups and saucers. I used
To select a cup and saucer I coloured the letters black and crossed
the same thing off in all the other squares. If the thing I chose
was AB then I would also cross off the A-somethings from same line
and row, and I would also cross off the something-Bs from same line
I started off by putting AA, BB, CC and DD on the top row. I wanted
a diagonal going down right of A-somethings and a diagonal going
down left of D-somethings.
In one square I had the choice of DA or DB so I chose one and
carried on. I noticed a pattern of 2 short diagonals of
C-somethings and B-somethings appearing. My dad helpd me with the
spredsheet and with this email.
These four solutions could be viewed