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?

assume each small square as a vertex of a 36-node graph.

using the information from the first table, we create edges between nodes in a row. two nodes are connected if they are represented by the same number in the row.

using the information from the 2nd table, we create edges between nodes in a column. two nodes are connected if they are represented by the same number in the column.

at the end, we will get 4 connected components of the graph.

if we count the number of nodes in those 4 componets we get

c1 - 19, c2 - 8, c3 - 1, c4 - 1.

hence no of green squares = the no of nodes in the largest component = 19.

 

Posted by Soumitra Pal on 2006-03-14 11:53:58