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This one drove me crazy for a while. Let's see how you do.


Three guys are driving cross country together, and stop in at a motel late one evening. The night manager tells them there's only one room left, and it costs $30. The guys are exhausted, so rather than drive on looking for a motel with separate rooms, they take the single and cough up $10 apiece.

The next morning the day manager looks at the books and sees that the guys were overcharged $5. He takes five dollar bills out of the cash register and gives them to the motel janitor to take to the three guys as a refund. On the way, the janitor pockets $2 for his troubles, and gives the three guys a dollar apiece.

After their refund the three guys only paid $9 each, or $27 total. But they gave the night manager $30, and the janitor only kept $2.

Where did the extra dollar go?

The answer is really simple, once you see it. You can read it, along with my attempt to explain it, below.



The short answer is that there is no "extra dollar." Another way of looking at it might be to say that the motel wound up with the "extra dollar," but that wouldn't be quite right.

You see, this little puzzle is really just an example of how slippery words can be. To make the problem a little less confusing, let's switch to numbers, instead.

There are two different ways of describing this story correctly.

  • Three guys pay $30 for a room. The hotel gets $25 after the refund, the guys keep the $3 refund, and the janitor pockets $2.

  • Three guys pay $9 each for a room, for a total of $27. The hotel gets $25,and the janitor pockets $2.
  • No problem there, right? If you reduce these two versions of the story to numerical equations, you get the following:

    • 30 = 25 + 3 + 2.

  • 27 = 25 + 2.
  • Still no problem. But the way the story is worded, you wind up confusing the two equations in your head. The story talks about the $30 the guys originally paid and the $27 they ended up paying after the discount, but those two numbers are from two different equations. The confusion arises from the suggestion that the two numbers 30 and 27 are somehow related, when they really aren't. And no matter how hard you try, you won't be able to use the $2 taken by the janitor (from either equation) to get 27 to equal 30 (see the figures in bold).

    Tomorrow the Cleveland Indians will meet the New York Yankees in the first round of the American League Playoff series. I was born and raised in Indian Country (northeast Ohio) and have rooted for the Tribe when they flat out sucked. Of course that made the good years in the 90's so much sweeter. Those teams were powerhouses, with amazing hitting. But with a few exceptions, they were not good defensive teams and the pitching staff was a group of aging overachievers.

    But the thing is: in baseball good pitching beats good hitting. A really great pitcher who cannot be hit by human beings. Oh you may get a single here and there, but when the guy on the mound has command and major stuff, batters whiff. In 1995 the Indians beat the pants off of most pitchers. But most pitchers aren't what you get in the playoffs. Teams rarely get to the playoffs with average pitching. Suddenly even the best hitters struggle, and in the playoffs the other team can hit pretty well too.

    So in many ways I like this years Indians team better than I did the World Series teams of 1995 and 1997. This team gets people out. They have the top pair of starters in baseball in C.C. Sabathia and Faustino Carmona. If Sabathia doesn't win the Cy Young Award it will be at travesty. In fact, three and four are pretty darned good too. These guys eat up innings and usually take the team late into the game Rafael Betancourt, closer Mike Borkowski and Rafael Perez make those late leads stick. The hitting is pretty good too, not like power-laden '95 but loaded with timely hitters who make tough outs. The Tribe is tied for the best record in baseball, winning 96 games this year. And Travis Hafner is finally getting hot. And when Pronk gets hot, baseballs fly.

    Yet when you look at all the scouting reports out there, nobody thinks the Indians will beat the Yankees. Nobody. After all, New York is the Best Team Money Can Buy. Faustino Carmona, so efficient at retiring hitters will wilt under the "patient Yankee hitters'. The Indians won't be able to hit Yankee pitching. The Yankees will hit the Tribe. When you look at the sports shows, everyone talks the National League (not surprising, since the Cubbies made the big dance, and Boston and the Yankees. The big market teams. If I hear the Tribe mentioned, it's only in passing.

    The simple fact is Cleveland may rock, but it gets no respect. It's a rust belt, blue collar town where the jobs are fading fast. No glamor like Boston or New York, where the media types live and want to do well. They don't want the Tribe to win. But baseball is an American game, and it's game of the Heartland as well as the media centers. The Indians are a likeable team, full of good people who play hard and don't treat their fans or other players like dirt. Manager Eric Wedge keeps his cool no matter what. And these guys like each other. Their payroll is just over half the Yankee payroll. The Cleveland Indians are the little guys, the real underdogs, the nice guys.

    So tomorrow night I intend to cook up a few hot dogs and coat them with onions and fiery hot stadium mustard. A cold beer is in order. And I really, really hope the team whose only believers are themselves goes out and whups Yankee butt.

    They deserve it. Hell, I deserve it.

    Game 1: Cleveland 12 New York 3. Apparently the Indians didn't listen to the prognosticators. One win does not a series make, but I like the start.

    Game 2. Cleveland 2 New York 1 (11) Remember the scout who said the 'patient Yankee hitters will force Carmona to bring the ball up'. He held them to 3 hits and one runs in nine innings. Rafael Perez set down six Yanks in a row to get the win. Granted the Indians could easily have lost and tossed away many chances to score (Andy Pettit might have had a hand in that) but we got the win. 2-0. I think they're taking the Tribe more seriously now.

    Game 3. Jake Westbrook didn't have a good day. Yanks did and win 8-4.

    Game 4. Indians pitcher Paul Byrd is treated like he's a crash test dummy before the game, as the press asks him if he's terrified. Like he didn't win 17 games this year. Apparently Byrd wasn't terrified as he beats the Yanks, allowing only 2 runs in five plus innings. Indians win the last game, 6-4 and the series against a team whose payroll is triple theirs.

    Do we get any respect? Some, but it's the day after and everyone's still talking about the Yankees.

    Sheesh.

    The Tampa Bay Rays have the second best record in the AL.  They are rarely on the tube

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