Professor Layton and the Eternal Diva

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Sunday, February 3, 2013

Puzzle No. 031
Picarats: 30


The distance three racehorses can run around the racetrack in one minute is listed below.

Horse A: Two laps.
Horse B: Three laps.
Horse C: Four laps.

The horses line up at the starting line and start running in the same direction. How many minutes will pass before all three horses line up at the starting line again?














Hint One: Someone in a hurry might jump to the conclusion that you need to find the lowest common multiple between the three numbers.

Read the problem over again and see if you can't clear things up for yourself.

Hint Two: The three horses each run at different speeds. To measure the horses' speeds, the problem tell you how many laps each horse can do in one minute.

The horses all run whole laps per minute, so at least you don't have to deal with strange speeds.

Hint Three: One horse runs two laps in one minute, and one runs four laps in one minute.

Where will the horses be one minute after they start running?

Solution:














You got it! In one minute, horse A will have done two laps, horse B will have done three laps, horse C will have done four laps, and all the horses will be line up at the starting line.