perplexus.info :: Logic : Veracity Verification II

Veracity Verification II (Posted on 2014-04-07)

Abram, Bruce and Carlo each make four statements about each other. However, precisely one of them made four true statements.

Abram said:
(1) Bruce owes me $10.
(2) Carlo owes me $5.
(3) All of Carlo's statements are true.
(4) All of Bruce's statements are false.

Bruce said:
(1) I owe no money to Abram.
(2) Carlo owes me $7.
(3) I am Norwegian.
(4) All Abram's statements are false.

Carlo said:
(1) I owe no money to anyone.
(2) Bruce is Spanish.
(3) I always tell the truth.
(4) Two of Bruce's statements are true and two are false.

Find which statements are true and which are false for all three.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Well, honestly ... (spoiler)

Comment 1 of 1

Well, clearly, A's statements are not all true, because A(3) would make C's statements all true, and this is a contradiction.

Assume C's statements are all true.

Then B2 and B3 are false, but C4 means that B1 and B4 are true.

But this is a contradiction, because A3 is true, which contradicts B4.

Therefore B's statements are all true.

Then from B4, all of A's are false.

Also, C1 is false (contradicts B2), C2 is false (contradicts b3), and C3 and C4 are false.

I see no contradictions, so this is the only solution.

To summarize, all of Bruce's statements are true, and all other statements are false.

Posted by Steve Herman on 2014-04-07 17:54:05

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