Puzzle | Gift in a Box

2.2

Three identical boxes are kept in front of you but only one of them has a GIFT inside. Each Box is labeled with a statement but only one of the statement is true
puzzle | Gift in a Box
Box 1 says the GIFT in this Box.
Box 2 says the GIFT not in this Box.
Box 3 says the GIFT not in Box 1.
Can you identify which Box has GIFT and which statement is true ?

Solution: Gift is in Box no. 2. Statement on Box no. 3 is true.
Explanation:
Analyze all statements one by one.

Case 1: Let Statement of Box-1 “GIFT in this Box” be true then Box 2 & 3 will be empty but Box-2 says the “GIFT not in this Box” which makes the statement true but puzzle says only one statement is true so clearly statement of Box-1 is invalid.
Case 2: If statement of Box-2 is true “Gift not in this Box” then other statements should be false according to puzzle. Statement of Box no. 3 says “GIFT not in Box no 1” which makes the statement of Box-3 true if the gift is in Box no. 3 and statement of Box no. 1 true if the gift is in Box no. 1. But according to puzzle only one statement is true so statement of Box-2 is also invalid.
Case 3: Let statement of Box-3 “GIFT not in Box-1” be true. Box-1 says “gift in this box” but since we assume statement of Box-3 is true and according to puzzle only one statement is true so statement of Box-1 is false and Gift is not in Box-1. Statement on Box-2 says “GIFT not in this box” but according to puzzle only one statement is true so this statement should be false which means gift is in Box-2. So, finally all conditions are full filled and we have found the gift is in Box-2 and statement of Box-3 is true.

References: https://www.youtube.com/watch?v=vwg87d8N3uM&t=53s
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