The rat and box puzzle.

Pic of question. 

Given conditions are (i) exactly one of the statements is true. (ii) exactly one box contains a rat.

By given conditions we solve it by three cases.


Case I- If first statement is true i.e., the rat is in box 1, then other two statements are false [by condition (i)] i.e., the rat is in box 2 and the rat is in box 1.
Which is a contradiction by condition (ii). [Since, exactly one box can contains a rat but here box 1 as well as box 2 contains rat. ]


Case II- If second statement is true i.e., the rat is not in box 2, then other two statements are false [by condition (i)] i.e., the rat is not in box 1 and the rat is in box 1.
Which is again a contradiction.


Case III- If third statement is true i.e., the rat is not in box 1, then other two statements are false [by condition (i)] i.e., the rat is not in box 1 and the rat is in box 2.
This case satisfied the condition (ii). 

Thus, the rat is in box 2. [By case III]


Hence, the answer is box 2.

 

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