### Brain Teasers

# Arthur Minit's Clock

Mad Ade was visiting his friend, computer tycoon and Olympic Kebab hurling champion, Mike Rohsopht.

He was there on Sunday and when the radio gave the time at the hour, Mad Ade noticed that the Madadian antique clock, designed by Madadian clock maker Arthur Minit (teaser #4891) was exactly 3 minutes slow.

"It loses 7 minutes every hour," said Mad Ade's friend. "No more and no less, but I've gotten used to it that way."

When Mad Ade spent a second evening with Mike Rohsopht later that same month, he remarked on the fact that the clock was dead right by radio time at the hour.

It was rather late in the evening, but Mike assured Mad Ade that his treasured Arthur Minit clock had not been adjusted nor fixed since his last visit.

What day of the week was Mad Ade's second visit?

He was there on Sunday and when the radio gave the time at the hour, Mad Ade noticed that the Madadian antique clock, designed by Madadian clock maker Arthur Minit (teaser #4891) was exactly 3 minutes slow.

"It loses 7 minutes every hour," said Mad Ade's friend. "No more and no less, but I've gotten used to it that way."

When Mad Ade spent a second evening with Mike Rohsopht later that same month, he remarked on the fact that the clock was dead right by radio time at the hour.

It was rather late in the evening, but Mike assured Mad Ade that his treasured Arthur Minit clock had not been adjusted nor fixed since his last visit.

What day of the week was Mad Ade's second visit?

### Answer

The answer is 17 days and 3 hours later, which would have been a Wednesday.This is the only other time in the same month when the two would agree at all.

In 17 days the slow clock loses 17*24*7 minutes = 2856 minutes, or 47 hours and 36 minutes. In 3 hours more it loses 21 minutes, so it has lost a total of 47 hours and 57 minutes. Modulo 12 hours, it has "gained" 3 minutes so as to make up the 3 minutes it was slow on Sunday. It is now (fortnight plus 3 days) exactly accurate.

Since the clock was not adjusted since the last visit, it's also possible that the radio time shifted by one hour due to a change to or from summer daylight saving time. However, it turns out that the only additional possibilities that need to be considered are those of 4 days 15 hours later, when the clock would have lost 12 hours 57 minutes, and 29 days 15 hours later, when the clock would have lost 3 days 10 hours 57 minutes. Without even considering the rules for when in the month the

clock is changed, these possible solutions are ruled out because we know that both visits were in the evening ("Mad Ade spent a second evening with Mike Rohsopht") and they involve times in a different part of the day.

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