Sunday Times Teaser 2631 – Family Progression

1. 
   brian gladman permalink

   Here is my solution

   Python

   from itertools import combinations months = ( 'January', 'February', 'March', 'April', 'May', 'June', 'July', 'August', 'September', 'October', 'November', 'December' ) # collect eligible times and dates dates = [] # for possible hours for hr in range(1, 12): # for possible months for mm in range(1, 13): # hour and month are two apart in the sequences so # valid differences are even and twice the increment inc, r = divmod(mm - hr, 2) if inc and not r: # form and check the validity of minutes, days and years mn, dd, yy = hr - inc, hr + inc, hr + 3 * inc if 0 < mn < 60 and 0 < dd < 32 and 0 < yy < 100: # form the sequence (minute, hour, day, month, year) t = (mn, hr, dd, mm, yy) # now check for sequences in which the sum of # two values equals the sum of the other three for p in combinations(t, 2): if 2 * sum(p) == sum(t): # store this sequence dates += [t] # now combine them five at a time for p in combinations(dates, 5): # check for a set of sequences in which both the # months and the years of birth are all different set_mm = set(x[3] for x in p) set_yy = set(x[4] for x in p) if len(set_mm) == len(set_yy) == 5: # sort the sequences by year of birth and extract the month q = [months[x[3] - 1] for x in sorted(p, key=lambda i:i[4])] # print the months of birth in age order print(' and '.join(', '.join(q).rsplit(', ', 1)))

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   from itertools import combinations   months = ( 'January', 'February', 'March', 'April', 'May',            'June', 'July', 'August', 'September',            'October', 'November', 'December' )   # collect eligible times and dates dates = [] # for possible hours for hr in range(1, 12):   # for possible months   for mm in range(1, 13):     # hour and month are two apart in the sequences so     # valid differences are even and twice the increment     inc, r = divmod(mm - hr, 2)     if inc and not r:       # form and check the validity of minutes, days and years       mn, dd, yy = hr - inc, hr + inc, hr + 3 * inc       if 0 < mn < 60 and 0 < dd < 32 and 0 < yy < 100:         # form the sequence (minute, hour, day, month, year)         t = (mn, hr, dd, mm, yy)         # now check for sequences in which the sum of         # two values equals the sum of the other three         for p in combinations(t, 2):           if 2 * sum(p) == sum(t):             # store this sequence             dates += [t]              # now combine them five at a time for p in combinations(dates, 5):   # check for a set of sequences in which both the   # months and the years of birth are all different   set_mm = set(x[3] for x in p)   set_yy = set(x[4] for x in p)   if len(set_mm) == len(set_yy) == 5:     # sort the sequences by year of birth and extract the month     q = [months[x[3] - 1] for x in sorted(p, key=lambda i:i[4])]     # print the months of birth in age order     print(' and '.join(', '.join(q).rsplit(', ', 1)))

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