Sunday Times Teaser 3291 – Top of the Pops
by Danny Roth
Published Sunday October 19 2025
George and Martha are keen pop music fans. They recently followed the progress of one record in the charts and noticed that it was in the Top Ten for three weeks in three different positions, the third week’s position being the highest. In practice, a record never zigzags; it reaches a peak and then drops. For example, 5,4,9 or 5,6,9 are possible but 2,5,3 is not.
“That’s interesting!” commented Martha. “If you add the three positions, you get the day of the month when my father was born and if you multiply them, you get a number giving the month and last two digits of that year.” “Furthermore,” added George “two of the positions also indicate the last two digits of that year.”
What were the three positions in chronological order, and what was the date of Martha’s father’s birth?
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BRG permalink123456789101112131415161718192021from itertools import combinations# the third week position is the highest in the charts# so must be the result of a rise (the three positions# are different); the prior change in position cannot# be a fall since a rise cannot follow a fall; so both# transitions must be rises which means that they form# a decreasing sequence in numeric terms# consider the three chart positionsfor a, b, c in combinations(range(10, 0, -1), 3):# the product is the month and the two digit yearm, yy = divmod(a * b * c, 100)if m:# the last two digits of the yearyt, yu = divmod(yy, 10)if yt != yu and {yt, yu}.issubset({a, b, c}):print(f"Positions: {a}, {b} and {c}; "f"Father's DoB: {a + b + c}/{m}/{yy}.")
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John Z permalink12345678910111213141516171819202122from itertools import combinations, permutations# consider possible weekly ratings, peaking at week three with no dipsfor wr in combinations(range(10, 0, -1), 3):# product of weekly ratingspwr = wr[0] * wr[1] * wr[2]# month and year from product of ratingsm, y = divmod(pwr, 100)# month must be 1-12if 13 > m > 0:# the two digits of the yeary10, y1 = divmod(y, 10)# are the two (different) digits of the year in the three weekly ratingsif len({y10, y1} & set(wr)) == 2:print('Ratings:', *wr, 'birthdate:', sum(wr), m, y)
