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 ?
(In reply to
Puzzle Answer by K Sengupta)
CASE 1: Both the the statements in Envelope 1 is true.
Then statement 2(a) is true but statement 2(b) is false, contradicting statement 1(a). Therefore, Envelope-2 contains one true and one false statement.
Hence, it follows that both the statements in Envelope 3 is false.
Since by 1(a), the formula is in Envelope 1, it follows that 3(a) is true, which is a contradiction. Consequently, Case-1 is invalid.
CASE 2: Both the statements in Envelope 3 is true.
Then, each of the statements 2(a) and 2(b) contradicts statement 3(b). Therefore both the statements in Envelope 2 is false.
Accordingly, statements 1(a) and 1(b) must be
Either, True and False in this order.
Or, False and True in this order.
If it is former, then truly stated statement 1(a) contradicts 3(b).
If it is latter, then the true statement 1(b) contradicts 3 (b).
Consequently, Case-2 is invalid.
CASE 3: Both the statements in Envelope 2 is true
Statements 3(a) and 3(b) contradicts statement 2(b). Therefore, both the statements in Envelope 3 is false.
Accordingly, {statement 1(a), statement 1(b)} == (false, true) or, (true, false)
If it is the former sub-case, then true statement 1(b) contradicts 2(b).
If it is the latter sub-case, then there is absolutely NO contradiction.
Accordingly, the formula is NOT contained in either of the Envelopes 1 or 2.
Consequently, the formula must be contained in Envelope 3.
Edited on June 13, 2022, 10:16 pm
Explanation to Puzzle Answer
