<p>Brown, Jones & Smith are suspected of income tax evasion.</p>

17.

Brown, Jones & Smith are suspected of income tax evasion.

Brown, Jones & Smith are suspected of income tax evasion. They testify, under oath as follows
Brown: Jones is guilty & Smith is innocent
Jones: If Brown is guilty, then so is Smith
Smith: I am innocent but at least one of the others is guilty.
a) Assuming everybody told the truth who is or are innocent or guilty?
b) Assuming the innocent told the truth & guilty lied who is or are innocent or guilty?

Submitted by tartle · Added 15 April 2011 · Updated 5 July 2026

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Solution:

Assuming everyone told the truth, Jones is guilty while Brown and Smith are innocent. Assuming the innocent tell the truth and the guilty lie, Brown and Smith are guilty while Jones is innocent.

Comments (3)

Anonymous 27 March 2011

The statements made by Brown, Jones, and Smith regarding their guilt or innocence are interesting. It would be helpful to clarify the assumptions about truthfulness.

Verglas ★ Solved 19 May 2011

a) Jones is guilty and the other 2 are innocent
b) Brown and Smith are guilty and Jones is innocent

Dzallen 11 July 2016

If lying means everything they say is false, then neither Brown nor Smith can be guilty (since one being guilty must mean the other is also guilty).

Therefore the answer for both cases is Jones is guilty, and Brown and Smith are innocent.

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