Home > Uncategorized > Up and Down the Mountain

Up and Down the Mountain

This post is motivated by the New York Times NumberPlay puzzle: The Princess Problem.

I was very late to this problem. The solution is very pleasing. It reminds me of the intermediate value theorem and the puzzle about meeting the monk on his journey up and down the meeting.

The puzzle can be visualized as a discrete Markov process:


I have plotted the strategy and 100 simulations of the journey through the rooms by the Princess. The horizontal axis is time. The vertical axis is the rooms. The purple “mountain” is the strategy and the red points are when the Prince successfully knocks (the first point of relevance). This is not a proof but a visual motivation towards one perhaps.


Note all all the even rooms are solved on the “ascent” and all the odd number rooms on the “descent”.

Categories: Uncategorized
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  1. March 30, 2015 at 6:09 pm

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