Aunt Jane had gone to a jumble sale and had brought a whole lot of cups and saucers, she's having many visitors these days and felt that she needed some more. You are staying with her and when she arrives home you help her to unpack the cups and saucers. There are four sets altogether. A set of white, a set of red, a set of blue and a set of green. In each set there are four cups and saucers. So as you can see there are 16 cups and 16 saucers altogether. Just for the fun of it you decide to mix them around a bit so that there are 16 different looking cup/saucers laid out on the table in a very long line.

So, for example :-

a) there is a red cup on a green saucer but not another the same although there is a green cup on a red saucer;
b) there is a red cup on a red saucer but that's the only one like it.

There are these 16 different cup/saucer combinations on the table and you think about arranging them in a big square. Because there are 16 you realise that there are going to be 4 rows with 4 in each row, [or if you like 4 rows and 4 columns.]

rows and columns teacup

So here is the challenge to start of this investigation. Place these 16 different combinations of cup/saucer in this 4 by 4 arrangement with the following rules:-

1) In any row there must only be one cup of each colour;
2) In any row there must only be one saucer of each colour;
3) In any column there must only be one cup of each colour;
4) In any column there must be only one saucer of each colour.

Remember that these 16 cup/saucers are all different so you CANNOT have a red cup on a green saucer somewhere and another red cup on a green saucer somewhere, and so on with all the colours.

There are a lot of different ways of approaching this challenge. Perhaps use some materials to help you [ paper, coloured paper, pens, crayons, sticky paper, multilink etc. etc.] You may like to make models of the cups and saucers.


When you think you have completed it check it through very carefully, it's even a good idea to get a friend who has seen the rules, to check it also.


Think about how you could change this challenge, and have a go at that one and then compare. You may see some relationships between similar problems in which a small change has been made.


Well again I wish you luck,

Bernard.