Alex visited Tom's cozy den one Sunday and they had the usual business of Tom's clock. When the radio gave the time at the hour the Ormulu antique was 3 minutes slow. "It loses seven minutes every hour" Tom told Alex as he had done so many times before. "No more, and no less, but I have gotten used to it that way."
When Alex spent a second evening with him later the 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 Tom assured him that his treasure had not been adjusted or fixed since his last visit.
What day of the week was the second visit?
There are 720 minutes in a 12 hour period.
After H hours, the clock will be 3 + 7H minutes slow.
If that expression is a multiple of 720, call it 720*K, the clock will read the correct time.
720 is 6 mod 7 or -1 mod 7.
3 + 7H is 3 mod 7
720K is 3 mod 7.
6K is 3 mod 7.
K can be {4, 11, 18, 25} any of 4 + 7x
3 + 7H = 720K; H = (720K - 3)/7
If K = 4, and 3 + 7H = 2880, then H = 2877/7 = 411 hours
So 411 hours after Sunday evening, the clock was correct.
That is 17.125 days later, so Wednesday 3 hours later in the evening.
If K is 11, then the clock was correct 1131 hours later (47.125 days later) which could not be in the same month.
Edited on March 13, 2024, 12:10 pm
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Posted by Larry
on 2024-03-13 12:09:49 |
Algebraic solution
