2x3 CheckerboardMath brain teasers require computations to solve.
There is a 2x3 checkerboard with 6 unit squares that are labeled as 1 through 6. If we are going to divide it into at least two rectangles whose sides are all integers, how many different ways are there?
HintSince the cells are labeled, ways that are the same upon reflection or symmetry are considered different ways.
AnswerThere are 33 different ways of dividing it.
4+2: 2 ways;
3+3: 1 way, 3 ways accumulated;
4+1+1: 2 ways, 5 ways accumulated;
3+2+1: 4 ways, 9 ways accumulated;
2+2+2: 3 ways, 12 ways accumulated;
3+1+1+1: 2 ways, 14 ways accumulated;
2+2+1+1: 11 ways, 25 ways accumulated;
2+1+1+1+1: 7 ways, 32 ways accumulated;
1+1+1+1+1+1: 1 way, 33 ways accumulated.
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