IBM Ponder This #098 · June 2006

Puzzle for June 2006.

Suppose we use dominoes to tile an infinite strip of height 2. In a typical tiling what fraction of the dominoes will be oriented vertically?  Typical can be defined rigorously by considering all possible tilings of a 2*n rectangle and then letting n go to infinity.

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The first 100 people who answer all parts correctly will be listed. The answer will be posted a week after the 100th is received, or at the end of the month.

Solution

Best opened after a real attempt

To be added.