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Tale of two clocks

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Two friends, whom we will call Arthur and Robert,

were curators at the Museum of American History.

Both were born in the month of May, one in 1932

and the other a year later.

Each was in charge of a beautiful antique clock.

Both of the clocks worked pretty well, considering

their ages, but one of them lost ten seconds an

hour and the other gained ten seconds an hour.

On one bright day in January, the two friends set

both clocks right at exactly 12 noon.

"You realize," said Arthur, "that the clocks will start

drifting apart, and they won't be together again until,

let's see, why, on the very day you will be 47 years

old. Am I right?" Robert then made a short calculation.

"That's right!" he said.


Who is older, Arthur or Robert?

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The clocks will be lined up again in 90 days. The only way to get from January to May in 90 days is from 1/30 to 5/1 on a leap year. Thus, Robert's birthday was in 1933 (turning 47 in 1980) and Arthur is one year older.

Almost, ndd. 90 days is only possible from 31 January to 1 May when February has 28 days. Thus Robert is turning 47 in a non-leap year which is 1979 and therefore Robert is older than Arthur.

Edited by Caliban27
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The clocks will be lined up again in 90 days. The only way to get from January to May in 90 days is from 1/30 to 5/1 on a leap year. Thus, Robert's birthday was in 1933 (turning 47 in 1980) and Arthur is one year older.

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First, these are old analog clocks, which means that there is no differentiation between AM and PM. Therefore, we are looking for the time when the two clocks, combined, get 12 hours out of sync.



There are 43,200 seconds in 12 hours
At a 20 second difference per hour over 24 hours, the difference will be 480 hours per day.
If the clock gets off by 480 seconds in a day it will take 90 days to get off by 12 hours, and thus back in sync.

If they set the clocks on Jan 31st, then during a non-leap year, the time until May 1st would be 90 days (28 in Feb + 31 Mar + 30 Apr + 1 May).

Leap year happens every 4 years, and it adds an extra day to that total (91 days). Therefore, it is impossible for the clocks to be set in January, and realign in May, during a leap year.


Additionally, 1932 was a leap year. This means that whomever was born in 1933 would turn 47 in 1980 (another leap year, as the difference between 1980 and 1932 is 48, which is a multiple of 4).

IF Robert were born in 1933, he would be turning 27 on a leap year. As previously established, we cannot make it from Janurary to May within 90 days on a leap year. Therefore, the current year must be 1979, and Robert must be born in 1932.

Thus, Robert is older than Arthur, who was born in 1933.

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