### Brain Teasers

# Liar Liar

Mad Ade's cousin Steve lies a lot. He tells the truth on only one day in a week.

One day he said: "I lie on Mondays and Tuesdays."

The next day he said: "Today is either Sunday, Saturday, or Thursday."

The next day he said: "I lie on Fridays and Wednesdays."

On which day of the week does Steve tell the truth?

One day he said: "I lie on Mondays and Tuesdays."

The next day he said: "Today is either Sunday, Saturday, or Thursday."

The next day he said: "I lie on Fridays and Wednesdays."

On which day of the week does Steve tell the truth?

### Answer

Mad Ade's cousin Steve tells the truth on TuesdaysThe first and third statements are incompatible; they cannot of course both be true, and they can only be lies if on one of the days mentioned Steve tells the truth. But, they have no such day in common. Therefore one of them must be true, and the other must refer to that day. Looking at the second statement (which must be a lie, as there can at most be one true statement and we have one), the first day cannot be Wednesday, Friday or Saturday. Therefore, the first statement cannot be true, since the third cannot refer to it by day. Therefore, the third statement is true, and must (from the first statement) be a Monday or Tuesday. Statement two, however, rules out Monday, leaving only Tuesday as the 'day of truth'. Thus: 'one day' is a Sunday; on the third day (Tuesday) Steve is truthful.

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## Comments

For once, we have a legitimate logic puzzle that is not in the Logic category,

instead of all the non-logic puzzles that wind up there!

Nice puzzle, well done.

instead of all the non-logic puzzles that wind up there!

Nice puzzle, well done.

Odd indeed. Very... cool though.

I'd be lying if I said I worked it out. It was fun but too hard at this time of night.

wowzaa. I'll just beleive you when you say it makes sense

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