Magical mystery box

Logic Level 2

There are 3 boxes, exactly one of which has the toy. A small girl is trying to get the toy but she can only open one box. Which box should she choose to get the toy?

On each box there is a statement, exactly one of which is true.

Box 1 says " The toy is in this box "

Box 2 says " The toy is not in this box "

Box 3 says " The toy is not in Box 1 "

Which box has the toy?

None of them Not enough information Box 2 Box 3 Box 1

2 solutions

Syed Hamza Khalid
Sep 3, 2017

We are told that only one of the statement is true .

$\Rightarrow \!\,$ If we state that the toy is in box 1 then 2 statements are true {Box 1 and Box 2} and 1 statement is false {Box 3} = Wrong because only one should be true.

$\Rightarrow \!\,$ If we state that the toy is in box 2 then 1 statements are true {Box 3} and 2 statement is false {Box 2 and Box 1} = Correct because only one is true.

$\Rightarrow \!\,$ If we state that the toy is in box 3 then 2 statements are true {Box 2 and Box 3} and 1 statement is false {Box 1} = Wrong because only one should be true.

$\Rightarrow \!\,$ So the only choice is box 2......

Denton Young
Feb 1, 2019

The statements on Box 1 and Box 3 are opposites, so one of them has to be the true statement. Therefore the statement on Box 2 must be false.

So the toy is in Box 2.

Magical mystery box

2 solutions

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