Sunday Times Teaser 3080 – One of a Kind
by Andrew Skidmore
Published Sunday October 03 2021
The raffle tickets at the Mathematical Society Dinner were numbered from 1 to 1000. There were four winning tickets and together they used each of the digits from 0 to 9 once only. The winning numbers could be classified uniquely as one square, one cube, one prime and one triangular number. For example, 36 is a triangular number as 1+2+3+4+5+6+7+8 = 36, but it cannot be a winner as 36 is also a square. The tickets were all sold in strips of five, and two of the winning numbers were from consecutive strips. The first prize was won by the holder of the smallest-numbered winning ticket, which was not a cube.
List the four winning numbers in ascending order.