Originally posted by Seifer28:
Garfield 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, its Thursday, Saturday or Sunday.
Day 3: I lie on Wednesday and Friday.
On which day does Garfield tell the truth????
Lets take day 1 as the truthful day. This means that day 2 and day 3 are lying days. Day 2 is a lying day which means day 2 must be a monday, wednesday or a friday. Day 3 is a lying day which means either Wednesday or Friday is a truthful day.
If Wednesday is the truthful day, it is Day 1. Which means day 2 has to be a thursday but look above? Day 2 must be a monday, wednesday or friday. so Wednesday is not the truthful day.
If Friday is the truthful day, which is Day 1, Day 2 is a saturday, look above again. Not possible so Friday is not the truthful day.
Combination of day 1 truthful and day 3 lying is not possible, therefore concluded that Day 1 is NOT the truthful day.
Day 2 as truthful day? Means day 1 and day 3 are lying days. Day 1 is a lying day which means either monday or tuesday is a truthful day. Day 3 is also a lying day which means either Wednesday or Friday is a truthful day. Therefore, day 2 being a truthful day is not possible.
This means Day 3 is the truthful day. This means day 1 and day 2 are lying days. Day 1 is a lying day which means either monday or tuesday is a truthful day. Day 2 is a lying day which means day 2 must be a monday, wednesday or a friday.
Now can see already. Day 3 is either a monday or tuesday because day 1 is a lying day. If day 3 is a monday, that makes day 2 a tuesday but its not.(see above). If day 3 is a tuesday, that makes day 2 a monday, which is possible(see above), and day 1 a sunday.
Therefore, the conclusion is that Garfield tells the truth on Day 3 which is a Tuesday.