A semi-minimalist painter created a work which consisted of a 6 x 6 array of small colored squares. Each small square contained just one color.

At the art gallery, six girl students were examining the painting. Each girl chose to report on exactly one horizontal row of small squares, by assigning a different number to each color in that row. The six row patterns, in the original order, were

121341
112213
123221
121222
122113
122134

The girls did not consult one another, so a given digit in one row does not necessarily represent the same color as the same digit in a different row.

Another group of six girls did the same process, but this time for the columns, rather than the rows. The column patterns they came up with look like this (but the array below shows the columns in no particular order):

1  1  1  1  1  1
2  1  2  2  1  2
3  2  3  2  2  2
4  3  2  2  3  1
3  2  1  2  4  2
2  4  1  3  3  2

Remember: the rows in the first table are shown in the correct order, but the columns in the second table are shown randomly. Outside of the particular row, for the first table, or column for the second table, do not expect the same digit-to-color coding scheme.

There were more green squares than any other color. How many squares were painted green?

(In reply to re(2): Solution by tomarken)

Actually, you could add a fifth color.  For example, the "4" in the top row, or the "4" in the bottom row, could be made a different color (say, purple) from the others, and it wouldn't change the solution because there are no other "purple" squares in that row or column.  However, this is a trivial difference, it doesn't change the fact that there are still 13 green squares. 

Whether or not there is a way that uses 5 or more colors, and changes the solution of 13 green squares, I'm not sure.  My gut feeling is no - as I solved it, I used the assumption that there were only 4 colors to help me fill in some of the sqaures (for example, "1 is red, 2 is green, 3 is blue, so 4 MUST be yellow", etc.)

Posted by tomarken on 2006-03-14 14:59:17