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?
behind=3; h=0;
while behind>0
h=h+1;
behind=behind+7;
if behind>=1440
behind=behind-1440;
end
end
disp([h h/24])
finds
411 hours after the first visit, or 17.125 days, the clock has lost 3 less than a multiple of 1440 hours and is thus equivalent to being exact.
17 days is congruent to 3 mod 7, so it's a Wednesday, and it's 1/8 day or 3 hours later in the evening than the moment in the first visit.
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Posted by Charlie
on 2024-03-13 11:32:37 |
computer solution (spoiler)
