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Envelopes (Posted on 2003-04-10) Difficulty: 2 of 5
There are three envelopes and exactly two statements are written on each of the envelopes. The statements on one of the envelopes are BOTH TRUE, the statements on the other envelope are BOTH FALSE and the remaining envelope has ONE TRUE and ONE FALSE statement. Here is what is written on the three envelopes:

First Envelope:
(a)The formula is not in here.
(b)The formula is in Envelope 2.

Second Envelope:
(a)The formula is not in Envelope 1.
(b)The formula is in Envelope 3.

Third Envelope:
(a)The formula is not in here.
(b)The formula is in Envelope 1.

Which envelope contains the formula ?

  Submitted by Ravi Raja    
Rating: 2.9091 (11 votes)
Solution: (Hide)
Let us assume that the Formula is in Envelope 1. In that case both the statements on the First Envelope as well as on the Second Envelope are False, violating the given conditions of the problem. So the Formula is not in Envelope 1.
(Since the problem states that : "The statements on one of the envelopes are BOTH TRUE, the statements on the other envelope are BOTH FALSE and the remaining envelope has ONE TRUE and ONE FALSE statement").

Next assume that the Formula is in Envelope 2. In this case we see that one statement written on each of the Second and Third envelopes is True and the other is False. Again violating the given conditions of the problem. So the Formula is not in Envelope 2.

Finally let us assume that the Formula is in Envelope 3. Now we see that the statement (a) on the First Envelope is True whereas statement (b) is False. Both the statements on the Second Envelope are True and both the statements written on the Third Envelope are False, thus satisfying all the conditions of the problem.

Hence we conclude that the Formula is in Envelope 3.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionExplanation to Puzzle AnswerK Sengupta2022-06-13 22:08:43
Puzzle AnswerK Sengupta2022-06-13 11:31:35
SolutionSolution without using case-by-case analysisBrian Smith2017-01-02 14:03:56
A different methodGamer2008-04-06 15:20:38
SolutionSearch, FindFrankM2008-04-06 09:37:32
AnswerPraneeth2007-08-29 06:45:12
SolutionBob2005-03-09 22:24:24
I got itJohn2004-09-19 03:27:30
SolutionSolutionLewis2003-07-25 22:26:41
re(4): this is easyRavi Raja2003-04-30 19:34:10
re(3): this is easyMichael2003-04-23 23:10:16
Explanation...Tim Axoy2003-04-17 11:33:26
re(2): this is easyRavi Raja2003-04-15 21:57:40
re: this is easyRavi Raja2003-04-15 21:45:24
re: this is easySteven2003-04-15 06:53:38
this is easytony2003-04-14 10:38:09
re: 1 and 2,true and true.Ravi Raja2003-04-13 04:54:38
re: Hunting for the formulaRavi Raja2003-04-13 04:48:23
re: HAHA! i think i got itRavi Raja2003-04-13 04:44:30
Solution1 and 2,true and true.Tim Axoy2003-04-13 04:21:59
re(2): SolutionRavi Raja2003-04-13 04:19:49
SolutionHunting for the formulaTim Axoy2003-04-13 04:18:55
re: My thoughtRavi Raja2003-04-13 04:15:20
re(2): Is it that straightforward?Ravi Raja2003-04-13 04:07:12
re: Is it that straightforward?Ravi Raja2003-04-13 04:05:20
SolutionHAHA! i think i got itSteven2003-04-12 20:13:52
re: solutionSteven2003-04-12 20:03:27
re: Solutionjohn2003-04-12 15:42:41
re: easy way to solve this type of problemjohn2003-04-12 15:38:49
My thoughtJessica Price2003-04-11 21:04:38
re: Is it that straightforward?Andrew F2003-04-11 17:30:45
Is it that straightforward?Andrew F2003-04-11 17:20:55
re: solutionRavi Raja2003-04-10 22:24:08
easy way to solve this type of problemJon2003-04-10 10:03:22
re: solutionaustin2003-04-10 08:19:19
solutionaustin2003-04-10 08:13:20
entertainingThe Mighty Puck2003-04-10 06:45:27
SolutionanswerDuCk2003-04-10 03:08:08
SolutionSolutionDJ2003-04-10 02:51:15
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