The Distance a Batter Travels When Running a Run in Cricket: A Puzzle

The Distance a Batter Travels When Running a Run in Cricket: A Puzzle

The Distance a Batter Travels When Running a Run in Cricket

In cricket, the distance a batter travels when running a run is not the full length of the pitch (22 yards). Instead, it is the distance between the two creases, which is 58 feet. However, even this distance is not always traveled in its entirety. The run is completed the moment the batter grounds his or her bat across the crease.

When batters run two, things happen differently. Each batter runs towards the opposite end, stretches the bat across the crease, and then turns back to their original end. The first run is completed after running some distance less than 58 feet. Taller cricketers can stretch their bat earlier, thereby running a shorter distance than shorter batters.

Puzzle:

Two batters of the same height are running two. The non-striker is the faster runner. They cross each other at a point that is 23 feet from the striker’s crease. The non-striker completes the first run first, stretching her arm across so that her bat crosses the crease, and turns back in the same motion without losing time, momentum, or speed.

Seconds later, the striker completes the first run in similar fashion, stretching her bat across after having run exactly the same distance as the non-striker had traveled for the first run. She too turns around for the second run without any loss of time or speed.

During the second run, the two cross at another point, which is 16 feet from the non-striker’s original crease. What distance did each batter travel in order to complete the first run?