Sunday Times Teaser 2623 – Latecomer

by Robin Nayler

Published: 30 December 2012 (link)

Imogen is having a New Year party tomorrow night and she has invited Madeline, hoping not to have a repeat of last year’s episode which completely spoilt the celebrations. Last New Year’s Eve Madeline had been due at a certain whole number of minutes past an hour but she was late, the number of minutes late being that same aforementioned “certain number of minutes” but with the digits in the reverse order. Madeline pointed out that at least the angle between the hands of the clock at the moment of her arrival was the same as it would have been when she was due.

At what time was she due to arrive?

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Brian Gladman permalink

An easy one this week (my thanks to Guy Walker for pointing out an error in my earlier version).


fs = 'Expected at {:d}:{:d} (arrived at {:d}:{:d}).'
# the expected hour of arrival (before 10PM could not spoil the event)
for h1 in range(10, 12):
  # the expected minute of arrival
  for m1 in range(1, 60):
    # the actual hour and minute of arrival 
    h2, m2 = divmod(60 * h1 + 11 * sum(divmod(m1, 10)), 60)
    # check for the same angles between the hands at the two times
    if abs(60 * h1 - 11 * m1) == abs(60 * (h2 % 12) - 11 * m2):
      print(fs.format(h1, m1, h2, m2))

fs = 'Expected at {:d}:{:d} (arrived at {:d}:{:d}).'

# the expected hour of arrival (before 10PM could not spoil the event)

for h1 in range(10, 12):

# the expected minute of arrival

for m1 in range(1, 60):

# the actual hour and minute of arrival

h2, m2 = divmod(60 * h1 + 11 * sum(divmod(m1, 10)), 60)

# check for the same angles between the hands at the two times

if abs(60 * h1 - 11 * m1) == abs(60 * (h2 % 12) - 11 * m2):

print(fs.format(h1, m1, h2, m2))

Sunday Times Teaser 2623 – Latecomer

by Robin Nayler

Published: 30 December 2012 (link)

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