# Richard and truth lie puzzle

Richard is a strange liar. He lies on six days of the week, but on the seventh day, he always tells the truth. He made the following statements on three successive days:

**Day 1:** “I lie on Monday and Tuesday.”

**Day 2:** “Today, it’s Thursday, Saturday, or Sunday.”

**Day 3:** “I lie on Wednesday and Friday.”

On which day does Richard tell the truth?

**Answer** –** Tuesday**

**Explanation:
**We know that Richard tells the truth on only a single day of the week

**.**

– If the statement on day 1 is untrue, This means that he tells the truth on Monday or Tuesday.

– If the statement on day 3 is untrue, This means that he tells the truth on Wednesday or Friday.

Since, Richard tells the truth on only one day, these statements

*.*

**cannot both be untrue**So, Exactly one of these statements *must be true*, and the statement on day 2 must be untrue.

Assume that,

The statement on day 1 is true. Then the statement on day 3 must be untrue, from which follows that Richard tells the truth on Wednesday or Friday. So, day 1 is a Wednesday or a Friday. Therefore, day 2 is a Thursday or a Saturday. However, this would imply that the statement on day 2 is true**, which is impossible.**

*From this we can conclude that the statement on day 1 must be untrue.*

This means that Richard told the truth on day 3 and that this day is a Monday or a Tuesday. So day 2 is a Sunday or a Monday. Because the statement on day 2 must be untrue, we can conclude that day 2 is a Monday. So day 3 is a Tuesday.

Therefore, the day on which Richard tells the truth is **Tuesday**.

### Your Answer

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