Cricket in the shadows
The puzzle
The geometry of the Earth lends itself to mathematical puzzles. Here is one that I composed.
Some years ago, the story goes, I was umpiring an adult league cricket match on a clear sunny day. As I was about to place the bails on top of the stumps at the start of the match, I perceived that the shadow of the middle stump just reached the popping crease. Some hours later, immediately after removing the bails for the lunch interval, I perceived again that the shadow of the middle stump just reached the popping crease. Some hours later again, immediately after removing the bails at the end of the match, I perceived for the third time that the shadow of the middle stump just reached the popping crease. The stumps were, of course, perfectly vertical. All you have to do is answer the following four questions.
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In what compass direction did the pitch run?
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At which end of the pitch was I umpiring?
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What was the date in the year, give or take a day or so?
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Where in the world did the match take place?
If you are unfamiliar with cricket, you need a picture. Even if you are thoroughly knowledgeable about cricket, it may be that you could still do with some measurements. See Figure 1.
Following the convention for puzzles of this kind, you may make use of real‐world facts in the public domain, for example that adult league cricket is played only on land and not in the middle of oceans.