Matchstick Math

Nov 24, 2001

RAY: Get out a bunch of matches and construct the following equation with Roman numerals:

One minus three equals -- using two match sticks to make the equals sign -- equals two.

Editor's note: this being the Car Talk Puzzler Psychic Friends Network, we can actually diagram this puzzler as...  I - III = II

RAY: Now, if the equation were three minus one equals two, that would be pretty good. But it's not.

The question is, what's the fewest number of match stick movements you can make to make an equation that's correct? You're not allowed to bend, fold, staple or mutilate any of the matchsticks, but you can move them, and you must use all the matches.


RAY: Here's the answer moving a match stick, one match stick. And that is, you take the match stick from the equal sign.

TOM: Yeah, yeah.

RAY: And you bring it over to where the minus sign is and you make one equal to three, now minus two.

TOM: Sure, that's good.

RAY: OK? Or, you move no sticks and you walk around to the other side of the table. You walk around 180 degrees --

TOM: Right.

RAY: -- and look at it from the other side of the table --

TOM: Yeah.

RAY: -- assuming you had them set up on a table. And you can look at it from the other side --

TOM: Yeah.

RAY: -- in which case you need to move nothing.

TOM: Well then, that's the right answer.

RAY: And it says two equals three minus one.

TOM: Well, the answer is what's the least number of --

RAY: Match stick movements.

TOM: Isn't zero leaster than one?

RAY: Yeah.

TOM: There aren't two answers. There's one answer.


TOM: The answer is zero.

RAY: In which case I already used it.

TOM: I know you did.

RAY: But it was a long time ago and everyone forgets. Anyway, do we have a legitimate winner?

TOM: Yes, we do. The winner is Richard King from Sunnyvale, California.

Get the Car Talk Newsletter