Sunday Times Teaser 3101 – Lap Progression
by Mark Valentine
Published Sunday February 27 2022 (link)
In a charity fundraising drive, two friends completed laps of their local track. Alan, a cyclist, raised £1 for his first lap, £2 for the second, £3 for the third and so on, with each extra lap earning £1 more than the prior. Bob, who walks, raised £1 for his first lap, £2 for the second, £4 for the third and so on, with each extra lap earning double the prior. Starting together, they travelled at constant speeds, and finished their last lap simultaneously.
After they had added up their totals, they were surprised to find they each raised an identical four-figure sum.
Including the beginning and end of their drive, how many times did Alan and Bob cross the lap start-finish line together?