This problem comes from the “Problems Drive” section of the Eureka magazine published in 1955 by the Archimedeans at Cambridge University, England. (“The problems drive is a competition conducted annually by the Archimedeans. Competitors work in pairs and are allowed five minutes per question ….”)
“There are ten times as many seconds remaining in the hour as there are minutes remaining in the day. There are half as many minutes remaining in the day as there will be hours remaining in the week at the end of the day. What time is it on what day?”
One of the hardest parts of the problem is just being able to translate the statements into mathematical terms. Solvable in 5 minutes?!!!
See the Hard Time Conundrum