How Many Cars
Car Talk 2007.02.18

Bugsy's Car Collection

RAY: Last week before the show we were talking about Bugsy's car collection. For the twenty plus years that we've known him, Bugsy has regaled us with tales about his Corvette restoration, his '63 Lincoln Continental Limo and lots of other classic cars that we've never seen and his wife didn't know he owned, until today. So we're sitting there and Tommy makes the following statement, 'Bugsy owns 50 cars. Maybe even more.'

Dougie says, 'No way. I know for sure that he owns fewer than 50 cars.'

Louie Cronin says, 'I know he owns at least one car.'

So Tommy says, 'Bugsy owns 50 cars, maybe more.' Berman says, 'No, no, no, he owns fewer than 50 cars, I know that for sure.' And Cronin says, 'I know one thing, he owns at least one car.'

Only one of these statements is true. How many cars does Bugsy really own?

Bugsy's Car Collection SOLUTION

Dougie is correct.  And the number of cars that Bugsy owns --- ZERO (0) CARS!

To see this consider the following graphic:

The solid red dots represent the places where each statement MAY BE TRUE.  We see that it is the case that only one statement has a chance of uniquely being true.  That is Dougie's statement and the place it can be true is when the number of cars is ZERO!  (Note there is only ONE value in the true range that only belongs to one statement).

To see this without considering a graphic:

Dougie is right and Bugsy has ZERO cars!

Dougie says that N<50 (fewer than 50 cars), this comes out to be 0, 1, ... 49 that is some number between zero and forty nine inclusive.

Louie says that N>=1 (at least one car), this comes out to be 1, ..., 49, 50, ... up to some maximum number.

Tommy says that N>=50 (fifty or more cars), this comes out to be 50, 51, ... up to some maximum number.

Dougie is the only one who has a chance of being uniquely true and further that value is ZERO.

The reason is that ZERO is the only number that only belongs to ONE statement.


from ..... "MMailLe@CarTalk.COM"
to ....... Zach.D.Cox@GMail.COM
date ..... Feb 19, 2007 12:10 PM
subject .. Thanks for contacting Car Talk

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Tom and Ray Magliozzi
Click and Clack the Tappet Brothers

This Page Last Update Tuesday, February 20, 2007 12:00:44 -0500