Bridge Crossing in Minimal Time

A family is trapped in a jungle. There is a bridge which can lead them to safety. But at one time, the bridge can only allow two people to pass through. Also, all of them are afraid of the dark and thus, they can't go alone.

Father takes 1 minute to cross, the mother takes 2 minutes, the son takes 4 and the daughter takes 5 minutes. While crossing the time taken will be according to the slower one. How can they all reach the other side in the minimum possible time?




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The responses of all the suspects are mentioned below.

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Peter was in the 2nd bedroom.
So was I.
David was in the bathroom.

Mandy:
I agree with Joseph that David was in the bathroom and Peter was in the 2nd bedroom.
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Peter:
Mandy was in the kitchen with Christopher.
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David:
I still say Peter was in the 2nd bedroom and Jennifer was in the bathroom.
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Jennifer:
Peter was in the bathroom with Christopher.
And Mandy was in the kitchen.

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David was in the kitchen.
And I was in the 2nd bedroom with Peter.

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Challenging

There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.