Sunday Times Teaser 3038 – Progressive Raffle
by Danny Roth
Published Sunday December 13 2020 (link)
George and Martha were participating in the local village raffle. 1000 tickets were sold, numbered normally from 1 to 1000, and they bought five each. George noticed that the lowest-numbered of his tickets was a single digit, then each subsequent number was the same multiple of the previous number, eg, 7 21 63 189 567. Martha’s lowest number was also a single digit, but her numbers proceeded with a constant difference, eg, 6 23 40 57 74. Each added together all their numbers and found the same sum. Furthermore, the total of all the digits in their ten numbers was a perfect square.
What was the highest numbered of the ten tickets?