Teaser 2750: Granny’s birthdays
From The Sunday Times, 7th June 2015 [link] [link]
At Granny’s birthday this year she was telling us some surprising things about some past birthdays. She told us that each year she writes down the date of her birthday (in the eight-digit form dd/mm/yyyy) and her age in years.
On two occasions in her lifetime it has turned out that this has involved writing each of the digits 0 to 9 exactly once. The first of these occasions was in 1974.
What is Granny’s date of birth (in the eight-digit form)?
Note that in order to solve this puzzle it is important to be aware of the date it was originally set.
All 200 puzzles included in the book The Sunday Times Brain Teasers Book 1 (2019) are now available on S2T2.
[teaser2750]
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Jim Randell 8:00 am on 6 October 2022 Permalink |
The puzzle was originally set on 7th June 2015, and mentions Granny’s birthday “this year” as having already happened. So her birthday must be earlier in the year than 7th June.
This Python program considers dates in 1974 up to 6th June, if the date includes 8 different digits, then the remaining 2 digits indicate Granny’s age (in some order), and we can then look for other years.
The program runs in 59ms. (Internal runtime is 4.3ms)
Run: [ @replit ]
from datetime import (date, timedelta) from enigma import (irange, repeat, nsplit, union, subsets, nconcat, printf) digits = set(irange(0, 9)) # consider dates earlier than this end = date(1974, 6, 7) # consider dates in 1974 inc = lambda x, i=timedelta(days=1): x + i for d in repeat(inc, date(1974, 1, 1)): if not (d < end): break # remaining digits ds4 = union([nsplit(d.month, 2), nsplit(d.day, 2)]) ds = digits.difference(nsplit(d.year, 4), ds4) if len(ds) != 2: continue # construct possible ages for ss in subsets(ds, size=2, select='P'): age = nconcat(ss) year = 1974 - age # collect "special" years years = list() for bd in irange(10, 99): y = year + bd if y > 2015: break if not digits.difference(nsplit(y, 4), ds4, nsplit(bd, 2)): years.append(y) if len(years) == 2 and years[0] == 1974: # output solution printf("{d} -> {years}", d=date(year, d.month, d.day).strftime("%d/%m/%Y"))Solution: Granny’s date of birth is: 26/05/1936.
So Granny is 38 in 1974 → (26/05/1974, 38).
And she is 47 in 1983 → (26/05/1983, 47).
In 2015 (when the puzzle was set) she was 79.
If we consider all dates in 1974 then there is a further solution of: 25/06/1936.
So, the puzzle only has a unique solution if posed between 27th May and 24th June. A fact that was not mentioned when the puzzle was included in the book The Sunday Times Brain Teasers 1 (2019).
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