Sunday Times Teaser 2509 – No Title
by Andrew Skidmore
Published October 24 2010 (link)
I won £10 on the lotto with three correct numbers (in the range 1 to 49).
I then calculated the difference between two six-figure numbers: one formed by writing my three winning numbers in descending order; the other by writing them in ascending order. I multiplied this difference by three and divided the answer by the sum of my winning numbers. I then divided the new answer by one of my winning numbers. The answer was another of my three winning numbers.
What, in ascending order, were my three winning numbers?
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Brian Gladman permalink123456789101112# 3^3.11.101.(a - c) = (a + b + c).(a.b or b.c or c.a)# Hence (a + b + c) = 101for a in range(1, 50):for b in range(a + 1, 51 - a // 2):c = 101 - (a + b)if c > b:t = 297 * abs(a - c)if t in {a * b, b * c, c * a}:print(f'Winning numbers: {a}, {b} and {c}.')
