Teaser 2475: [Stopped clock]
From The Sunday Times, 28th February 2010 [link]
“I see that our long case has stopped”, said Watson, who had been reading Holmes’s monograph on chronometers. “Is there anything significant about the time?” Holmes replied: “Apart from the obvious facts that just one hand is precisely on 12, and clockwise the hands are in the order “second” , “minute”, “hour”, I see that the time read as a 3- or 4-digit number is the product of two whole numbers, the larger of which is the number of minutes clockwise from the minute hand to the hour hand”.
At what time did the clock stop?
This puzzle was originally published with no title.
[teaser2473]
S2T2 
Jim Randell 10:12 am on 11 July 2025 Permalink |
If one of the hands is on the 12, then the clock must be showing an exact number of minutes, and so the second hand must be on 12.
Then as we go clockwise from the second hand we encounter the minute hand (which is on an exact minute marking), and then the hour hand (which must also be on an exact minute marking, so the number of minutes must be a multiple of 12).
This Python program considers possible hours and minutes, calculates the number of minute divisions the hour hand is ahead of the minute hand and then checks that this divides into the time (read as a 3- or 4-digit number) to give a smaller number.
It runs in 60ms. (Internal runtime is 46µs).
from enigma import (irange, cproduct, divc, div, printf) # possible hours and minutes (must be a multiple of 12) for (h, m) in cproduct([irange(1, 11), irange(12, 59, step=12)]): # number of minutes pointed to by the hour hand p = (5 * h) + (m // 12) # minute divisions the hour hand is ahead of the minute hand d = p - m if not (d > 0): continue # time read as a 3- or 4-digit number n = 100 * h + m r = div(n, d) if r is None or not (d > r): continue # output solution printf("{h:02d}:{m:02d} -> {n} = {d} * {r}")Solution: The clock stopped at 8:12.
The second hand points to 12 (= 0 minutes), the minute hand to 12 minutes, and the hour hand to 8 + 12/60 hours (= 41 minutes).
The hour hand is 29 minute divisions ahead of the minute hand, and: 812 = 29 × 28.
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