Weekly Lies
Mr Ross tells truths or lies depending on the day of the week. Can you catch him out?
Age
11 to 14
Challenge level
Problem
Mr Ross always tells the truth on Thursdays and Fridays but always tells lies on Tuesdays. On the other days of the week he tells the truth or tells lies, at random. For seven consecutive days he was asked what his name was, and on the first six days he gave the following answers, in order: John, Bob, John, Bob, Pit, Bob. What was his answer on the seventh day?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Mr Ross does not give the same name twice in a row, so the six days cannot include both Thursday and Friday. Therefore day 1 is a Friday or a Saturday.
If day 1 is Saturday, then he says his real name on Thursday (day 6), which is therefore Bob. But he also says Bob on Tuesday (day 4) the day when he definately lies, which is impossible, so day 1 must be a Friday.
In this case his name is John, and day 7 is a Thursday, a day on which he tells the truth. Therefore his answer on the seventh day will also be John.