Window has been broken!

Logic Level 3

Five children(boy or girl) were playing soccer, one of the five broke a window of a house. The house owner comes and asks them: Who broke the window? Each child made three statements , where two statements are true and one statement is false. Five boys/girls are, James, Mike, Vinny, Jack and Sara.

James:

• I didn't do it.

• Sara will tell who did it.

• One of us is in big trouble.

Mike:

• Jack did it.

• I didn't do it.

• I don't even like to play soccer.

Vinny:

• I didn't do it.

• Jack and I are good friends.

• Sara doesn't know who did it.

Jack:

• Mike lied when he said I broke the window.

• I never saw Vinny before.

• I never broke a window in my life.

Sara:

• I saw Jack break it.

• I didn't break the window.

• I want to go home.

Who broke the window?

Vinny Jack Mike Sara James

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1 solution

Jonathan Quarrie
Jun 30, 2017

If it was James

  • James: I didn't do it. = L i e \color{#D61F06}Lie
  • James: Sara will tell who did it. = L i e \color{#D61F06}Lie
    • Sara: I saw Jack break it. L i e \color{#D61F06}Lie

James would have told two lies (via Sara's lie), so it can't be him.


If it was Mike

  • Mike: Jack did it. = L i e \color{#D61F06}Lie
  • Mike: I didn't do it. = L i e \color{#D61F06}Lie

Mike would have told two lies, so it can't be him.


If it was Jack

  • Jack: Mike lied when he said I broke the window. = L i e \color{#D61F06}Lie
    • Mike: Jack did it. = T r u e \color{#20A900}True
  • Jack: I never broke a window in my life. = L i e \color{#D61F06}Lie

Jack would have told two lies (via Mike's truth), so it can't be him.


If it was Sara

  • Sara: I saw Jack break it. = L i e \color{#D61F06}Lie
  • Sara: I didn't break the window. = L i e \color{#D61F06}Lie

Sara would have told two lies, so it can't be her.


This leaves V i n n y \large\boxed{Vinny} as the culprit, because all of the others would have told two lies if it was them.

To confirm:

James Mike Vinny Jack Sara
I didn't do it. = T r u e \color{#20A900}True Jack did it. = L i e \color{#D61F06}Lie I didn't do it. = L i e \color{#D61F06}Lie Mike lied when he said I broke the window. = T r u e \color{#20A900}True I saw Jack break it. = L i e \color{#D61F06}Lie
Sara will tell who did it. = L i e \color{#D61F06}Lie I didn't do it. = T r u e \color{#20A900}True Jack and I are good friends. = T r u e \color{#20A900}True I never saw Vinny before. = L i e \color{#D61F06}Lie I didn't break the window. = T r u e \color{#20A900}True
One of us is in big trouble. = T r u e \color{#20A900}True I don't even like playing soccer. = T r u e \color{#20A900}True Sara doesn't know who did it. = T r u e \color{#20A900}True I never broke a window in my life. = T r u e \color{#20A900}True I want to go home. = T r u e \color{#20A900}True

There are a few statements that we can't necessarily prove as True or a Lie. We have to assume they are true until another statement contradicts it.

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