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One person tells the truth on Monday, Tuesday, Wednesday, and Thursday and lies on all other days of the week. A second person lies on Tuesday, Wednesday, and Thursday and tells the truth on all other days of the week. If today both people say "I lied yesterday", which day of the week is today?

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What happens if you ask one of these people "Is today one of your lying days?" –  paw88789 yesterday

4 Answers 4

Hint: what combinations of truth telling/lying today/yesterday allow one to say "I lied yesterday"? For example, you can't be telling the truth both days...

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Yes...i understand what you mean and i did the combination , but i could not define the exact day.Because the days of both people interact with each other.@Ross –  d.i... Feb 15 at 16:09
    
For each one individually, you should find two days of the week that each can say "I am lying". What did you find? There is only one day they can both say that. –  Ross Millikan Feb 15 at 16:11
    
@d.i... The days of the two people do not interact with each other. They are completely separate. Make a chart with seven boxes labeled Sunday, Monday, …, Saturday. In each box mark whether the first person lies on that day. Then figure out on which days the first person could say "I lied yesterday" and mark the chart. Then put the sheet away and start over for the second person. When you are finished, look at both sheets together. –  MJD Feb 15 at 16:13
    
Yes..thank you i tried that and it turned out to be that the day is friday @MJD –  d.i... Feb 15 at 16:35
    
That is correct. –  Ross Millikan Feb 15 at 16:36

Well, if the statement "I lied yesterday" uniquely picks out a day, then you can rule out Sat./Sun. as well as Wed./Thurs., because the truth/lies-telling propensities for either day in the pair (along with the prior day) are the same.

That leaves just Monday, Tuesday, and Friday, and you can just inspect each day. On Friday, person A will be lying about Thursday, on which he told the truth, so he will say "I lied yesterday". Person B will be telling the truth about his lie on Thursday, so he will say "I lied yesterday". So Friday it is.

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Today is Friday.

A lies on Friday , tells the truth on Thursday

A say's "I lied yesterday" , that's a lie because he told the truth yesterday so check.

B tells the truth on Friday , lies on Thursday

B say's "I lied yesterday" , that's true because he lied yesterday so check

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The sentence "I lied yesterday" can be uttered on two different days.

  1. When one lied yesterday but speaks the truth today.
  2. When one spoke the truth yesterday but lies today.

All other days make the sentence impossible, either because while lying yesterday, the speaker should lie today too, or if speaking the truth today, also spoke the truth yesterday.

Each person has two such days:

  1. Monday and Friday
  2. Tuesday and Friday

The only day in common, on which they both can say it, is Friday, the first person lying about speaking the truth yesterday, the second truthfully telling you that yesterday was a day of lies.

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