Sunday Times Teaser 3186 – Contemporary Classmates
by Edmund Marshall
Published Sunday October 15 2023 (link)
In our local school, the year begins on September 1 and ends on August 31, and class one contains all the children who reach the age of five during the school year. I was looking back at the school records and discovered that one year during the 1980s, it so happened that the birthdays of a group of children in class one fell on the same-numbered day of different months and also on the same day of the week. The size of this group was the largest possible for these circumstances, and by coincidence the number of classmates in the group was also the number of the day in the month for their birthday. The oldest member of that group, whose birthday was in January, was born in the 1980s.
What was the full date of birth of the youngest member of that group?
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BRG permalink12345678910111213141516171819202122232425262728293031from collections import defaultdictfrom datetime import date, timedelta# consider years in the 1980'sfor year in range(1980, 1989):# map[days of month, weekdays] -> list of class birthdaysdw2dts = defaultdict(list)# compile values for the current yeard = date(day=1, month=9, year=year)while True:dw2dts[d.day, d.weekday()] += [d]d += timedelta(days=1)if d.day == 1 and d.month == 9:break# find the class size for this yearclass_size = max(len(v) for v in dw2dts.values())for dts in dw2dts.values():if len(dts) == class_size:# oldest is born in January and the day in the month equals the class sizeif dts[0].month == 1 and dts[0].day == class_size:# find the birth dates (of which the oldest must be in the 1980's)bdays = list((d.day, d.month, d.year - 5) for d in dts)if bdays[0][2] >= 1980:t = ', '.join(f"{d[0]:02}/{d[1]:02}/{d[2]}" for d in bdays)f, s, l = t.rpartition(', ')print(f"Class birthdays: [{' and '.join((f, l))}].")
