Tale of two clocks in New Logic/Math Puzzles Posted December 14, 2012 · Report reply First, these are old analog clocks, which means that there is no differentiation between AM and PM. Therefore, we are looking for the time when the two clocks, combined, get 12 hours out of sync. There are 43,200 seconds in 12 hours At a 20 second difference per hour over 24 hours, the difference will be 480 hours per day. If the clock gets off by 480 seconds in a day it will take 90 days to get off by 12 hours, and thus back in sync. If they set the clocks on Jan 31st, then during a non-leap year, the time until May 1st would be 90 days (28 in Feb + 31 Mar + 30 Apr + 1 May). Leap year happens every 4 years, and it adds an extra day to that total (91 days). Therefore, it is impossible for the clocks to be set in January, and realign in May, during a leap year. Additionally, 1932 was a leap year. This means that whomever was born in 1933 would turn 47 in 1980 (another leap year, as the difference between 1980 and 1932 is 48, which is a multiple of 4). IF Robert were born in 1933, he would be turning 27 on a leap year. As previously established, we cannot make it from Janurary to May within 90 days on a leap year. Therefore, the current year must be 1979, and Robert must be born in 1932. Thus, Robert is older than Arthur, who was born in 1933.