Cricket in the shadows

A mathematical puzzle

Cricket in the shadows

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 again perceived 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. All you have to do is answer the following four questions.

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.

Figure 1: Some measurements in the game of cricket