By the time we dug out from under the mail last month, we had received more than 500 responses to the "missing dollar" puzzle. Not surprisingly, the first winning entries were submitted by e-mail. The first arrived at 5:12 a.m. on the day of publication! Obviously, you have to get up pretty early to fool Horizon readers.

The winners:

Michael Kelley, Berwyn Heights

John Beere, Manassass

David B. Bayliss, Woodbridge

Dick Huwel, Springfield

Charlie Reiher, Lanham

Antonio Zamora, Bethesda

Ian Band, District

Fran Doyle, Severna Park

Dean W. Smith, Kingstowne, Va.

John G. DeGooyer, Crownsville, Md.

Additionally, in an unaccustomed fit of fairness and generosity, we're also sending T-shirts to the first 10 letter-mail entries, based on postmark times on the envelopes.

For those unfortunates who missed it, the puzzle involves three men who arrive at a hotel. The only vacant room is priced at \$30. Each pays \$10 and goes up for the night. A while later, the desk clerk remembers that the room price is only \$25, so he gives the bellhop five \$1 bills as a refund for the men. On the way to their room, the bellhop pockets \$2, then gives each of the unwitting travelers a \$1 refund.

So each man paid only \$9 for the room, making a total of \$27. The bellhop kept two more, totaling \$29. Where is the missing dollar?

There are several ways to solve the puzzle "correctly." But all involve recognizing at least one of two things:

(1) There's something fishy about the statement that "each of the three men paid only \$9 for the room, making a total of \$27."

(2) There's something wrong with adding the bellhop's stolen \$2 to the travelers' \$27.

First, you can properly say that the room cost \$30 or \$25, but not \$27. Each of the three travelers initially paid \$10 for the room, making a total of \$30. The final, discounted payment for the room was \$25, or \$8.33 each. Each traveler got \$1 back and the bellhop stole \$2, for a total of \$30.

Saying the travelers "paid" \$27 for the room is literally incorrect and logically misleading.

But you can still do the math that way if you want. The actual net outlay from the men was \$27. But that amount includes the \$2 stolen by the bellhop. So it's wrong to add the bellhop's \$2 to the \$27.

Instead, to account for all of the money in circulation, you should add the \$3 the men now have to the \$27 they no longer have for a total of \$30.

Alternatively, you can subtract the bellhop's \$2 from the net payment of \$27. That, too, makes everything turn out right. The travelers gave the hotel \$25 and "gave" the bellhop \$2, for a total of \$27. And each traveler got \$1 back, for a total of \$30.

This month's puzzle is on Page H8.

Feedback Loop

Several readers wrote to complain, with alarm, that the "hydrogen beer" anecdote mentioned in a short sidebar with our Sept. 8 article on hydrogen is not true.

Indeed, Horizon did not undertake a comprehensive international investigation of the exploding brew matter before publication. Instead, we dutifully confirmed published accounts of the events in various name-brand newspapers, and our correspondent in Montreal also cited a TV show about the phenomenon.

We will, however, continue to probe this inflammatory area and report our findings when we find 'em.

Another batch of letters took exception to a parenthetical remark in a "How Come" question indicating that glass in some centuries-old windows had "run" over time, making them slightly thicker at the bottom than the top. Last time we checked, back in 1995, this was regarded as true by experts we consulted.

But reader Gregory Resch of Oxon Hill observed that "if the Horizon staff had been dutifully availing itself of readily accessible sources of scientific information, your writers and editors would likely have known of the article, `Analysis shatters cathedral glass myth' in Science News for May 30, 1998, which summarizes a scientific study (reported in the American Journal of Physics) disproving the flowing-window canard."

We have the profoundest respect for Science News, a wonderfully readable weekly magazine based in the District, and we recommend it to all. Including this item, from the article cited by Resch:

"Edgar Dutra Zanotto of the Federal University of Sao Carlos in Brazil calculated the time needed for viscous flow to change the thickness of different types of glass by a noticeable amount. Cathedral glass would require a period `well beyond the age of the universe,' he says."

The fact that the panes in some cathedral windows are plainly thicker at the bottom probably is a result of manufacturing techniques at the time, the magazine observed.