The Question
This week’s puzzle asked you which friend was older
Two friends, whom we will call Arthur and Robert, were museum curators. 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 realise," 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?
The Solution
If you do the calculation, it turns out that the clock will come back together in 90 days (since they're old fashioned 12-hour clocks). But now, the conversation takes place in January, and the birthday when they come back together is in May, and there are at least 89 days in February, March, and April (with 90 in a leap year). So, the only way that it can be May 90 days later is if (i) the conversation takes place on the last day of January, (ii) the birthday is on the first day of May, and (iii) it is not a leap year. The last part is the key, since that means that it can't be 1980 - so Robert, who is turning 47, can't have been born in 1933.
So, Robert was born in 1932, and is the older of the two.
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