A calendar of truth and lies: The Weekly Puzzle by Dilip D’Souza

There are plenty of puzzles about liars and truth-tellers

There are plenty of puzzles about liars and truth-tellers. You know, you meet two of them and don’t know which is which, but can you still, by asking one question, get them to point out the correct path to the nearest idli-dosai place?

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Here’s a variant of sorts. A family you know has twin daughters who are always dreaming up peculiar things to do. One day, their long-suffering mother tells you their latest: “Sabiya is a liar on Monday, Tuesday and Wednesday, but tells the truth every other day of the week. Manjiri lies on Thursday, Friday and Saturday, but it’s nothing but the truth on the other days of the week.”

Intrigued by this, you ask to meet the girls. When you do, Sabiya says: “Yesterday I told about 200 lies!” Manjiri pipes up: “Me too!”

Question: What day is it?

Scroll down for the answer.

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Solution and answer

First, note that on any given day of the week except Sunday, one girl is lying and one is telling the truth. If it is one of those days, one of the girls’ statements is a lie and the other true; if Sunday, both are true.

But wait, can both be true? On a Sunday, Manjiri’s statement is true (since she lies on Saturdays), but Sabiya’s cannot be (since she tells the truth on Saturdays).

Thus we know it’s not Sunday; and that one statement must be true and the other one a lie.

The true statement can only be true if it is made on a day that the girl concerned tells the truth, but immediately after a day when she lied. For Manjiri, that’s Sunday; for Sabiya, Thursday.

But we know it can’t be a Sunday. Thus it is a Thursday. So Manjiri is lying, Sabiya is telling the truth.