Lighthouse Flashes
Read the puzzle
A lighthouse flashes at evenly spaced times. From flash 1 to flash 6 takes 5 seconds. How many seconds pass from flash 1 to flash 11?
A lighthouse flashes evenly. From the 1st flash to the 6th takes 5 seconds. How long from the 1st flash to the 11th?
Count the gaps between flashes, not the flashes.
10 seconds
Flash 1 to flash 6 is 5 gaps, so each gap is 1 second. Flash 1 to 11 is 10 gaps.
How to solve it
Count gaps between flashes, not flashes.
Step one: from flash 1 to flash 6 there are 6 − 1 = 5 gaps. Those 5 gaps take 5 seconds, so each gap lasts 5 ÷ 5 = 1 second.
Step two: from flash 1 to flash 11 there are 11 − 1 = 10 gaps.
Step three: 10 gaps × 1 second = 10 seconds.
The common wrong answer is 11 seconds, from thinking "11 flashes, one second each". But the first flash starts the clock at 0 seconds, so it takes no time of its own. Another slip is to say each flash takes 5 ÷ 6 of a second, which mixes up flashes and gaps and gives a messy fraction.
Quick check: list the times. Flash 1 is at 0 s, flash 2 at 1 s, flash 6 at 5 s (matching the clue), and flash 11 at 10 s. Takeaway: this is the fence post idea in time, where flashes are posts and the seconds between them are the gaps.
Learn the method: Fence Post Riddle: Why a 15 m Fence Needs 6 Posts
