S2T2

Jim Randell 11:22 am on 4 July 2021 Permalink Reply
Tags: by: R Brain ( 3 )   

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  Jim Randell 11:23 am on 4 July 2021 Permalink | Reply

  This Python program runs in 54ms.

  Run: [ @replit ]

  from datetime import date, timedelta
  from enigma import dsum, printf
  
  # digit sum of a date
  ddsum = lambda d: dsum(d.day) + dsum(d.month) + dsum(d.year)
  
  # generate dates in a specific range
  inc1 = timedelta(days=1)
  def drange(a, b, step=inc1):
    while not(a > b):
      yield a
      a += step
  
  # consider date of next birthday (within 1 year of the puzzle date)
  for d in drange(date(1961, 12, 10), date(1962, 12, 9)):
    w = d.weekday()
    # must be a workday
    if w == 6: continue
    
    # calculate digit sum (= age)
    n = ddsum(d)
  
    # and calculate the date n years ago
    b = date(d.year - n, d.month, d.day)
  
    # do days of the week match?
    if b.weekday() == w:
  
      # if the birthday was 28 days later ...
      b_ = b + 28 * inc1
      # the digit sum of the nth birthday is also n
      if ddsum(date(b_.year + n, b_.month, b_.day)) == n:
        printf("{d} ({n}) -> born = {b} (+4w = {b_})")
  

  Solution: Gregory was born on Friday, 2nd February 1940.

  So:

  His next birthday, on Friday, 2nd February 1962, is his 22nd.
  And 2+2+1+9+6+2 = 22.

  If he had been born exactly 4 weeks later, it would have been, Friday, 1st March 1940.
  His next birthday, on Thursday, 1st March 1962, is his 22nd.
  And 1+3+1+9+6+2 = 22.

  There is a second candidate solution:

  Gregory was born on Sunday, 11th February 1940.
  His next birthday, on Sunday, 11th February 1962, is his 22nd.
  And 1+1+2+1+9+6+2 = 22.

  If he had been born exactly 4 weeks later, it would have been, Sunday, 10th March 1940.
  His next birthday, on Saturday, 10th March 1962, is his 22nd.
  And 1+0+3+1+9+6+2 = 22.

  But this is eliminated as his next birthday is on a Sunday, so he wouldn’t have to take the day off work.

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  Jim Olson 9:41 pm on 6 July 2021 Permalink | Reply

  Four weeks after 2/22/1940 would have been 3/21/1940.

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    Jim Randell 9:51 pm on 6 July 2021 Permalink | Reply

    But if he was born on 22nd February 1940 his next birthday in 1962 would be his 22nd, but the sum of the digits in the date (22/2/1962) would be 24, so it doesn’t work.

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  Jim Olson 10:06 pm on 6 July 2021 Permalink | Reply

  I think the wording of this Teaser through me off. I see that the 3/21/1962 digits don’t total 22 and that was my problem. 3/1/1940 is not four weeks after his birth. So I didn’t see how this satisfied the requirements of the teaser.

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    Jim Randell 10:40 pm on 6 July 2021 Permalink | Reply

    1st March 1940 is exactly 4 weeks after 2nd February 1962 because 1940 was a leap year. So the month number goes up 1 and the day number goes down 1, keeping the sum of the digits the same. (Of course the fact that 1962 is not a leap year means that if he had been born 4 weeks later, his next birthday would not be on the same day of the week as the day he was born. But the sum of the digits in the date would be the same as his age, and that is what is important).

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  Jim Olson 11:50 pm on 6 July 2021 Permalink | Reply

  Apologies I must of misread the posting of the answer as 2/22/1940.

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