ThatDonGuy
Joined: Jun 22, 2011
• Posts: 4676
April 19th, 2020 at 8:19:50 AM permalink
Inspired by the Wynn's new restriction of no more than four people in an elevator at once.
By the way, I don't know the answer to this one - at least, not yet...

"Apparently," the standard size of a hotel elevator is 80 inches wide and 65 inches from front to back.
Assume the door opening is 60 inches wide, centered on the long side.
Three people get into an empty elevator, one at a time.
What is the largest possible "clear space radius" that any of the three can maintain from when they get on until when they get off?
Assume that the order in which the three get on and off maximizes the answer.
Mosca
Joined: Dec 14, 2009
• Posts: 3813
April 19th, 2020 at 9:08:50 AM permalink
They form an equilateral triangle, with the first guy going to one of the far corners.
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ThatDonGuy
Joined: Jun 22, 2011
• Posts: 4676
April 19th, 2020 at 10:26:31 AM permalink
Quote: Mosca

They form an equilateral triangle, with the first guy going to one of the far corners.

I think the third person would be farther away from the other two if the first two were in the two far corners and the third was in the front, equidistant between the two side walls.

I have a feeling that, if the first person goes into a far corner, the second one goes against the other side wall but not quite all the way to the back, and the third stays as close to the front as possible but not quite centered, then the shortest distance between two of them would be larger.

rxwine
Joined: Feb 28, 2010
• Posts: 9997
Thanks for this post from:
April 19th, 2020 at 11:10:25 AM permalink
all 3 stand in the middle in a back to back triangle. The germs come out the mouth and nose.
Quasimodo? Does that name ring a bell?
billryan
Joined: Nov 2, 2009
• Posts: 10367
April 19th, 2020 at 11:39:24 AM permalink
Who pushes the button ?
In NYC, many places have what we call "Jewish" elevators. On the Sabbath, some Jews are not allowed tp use phones or push a button and the elevators are programmed to stop o every floor.
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 4676
April 19th, 2020 at 11:51:51 AM permalink
Quote: billryan

Who pushes the button ?
In NYC, many places have what we call "Jewish" elevators. On the Sabbath, some Jews are not allowed tp use phones or push a button and the elevators are programmed to stop o every floor.

It's probably like the elevators at Thed - er, The D - where you select a floor before you get in the elevator.

Let A be in the back left corner, B be in the back right corner, and C be in front, halfway between the two sides.
A and B are 80 inches apart; A and C are sqrt(652 + 402) = 76.322 inches apart, as are B and C.
If, say, C moves forward, then the distance from B to C is less than 76.322, unless C moves to the left, but this would make the distance from A to C less than 76.322.
Therefore, any solution requires that A and B be in the back somewhere.
Suppose B moves to the center of the back. The maximum distance from B to C that would be less than the distance from A to C is 76.322, when B is in the front right corner, but the distance from A to B is only 40.
Moving B to the left shortens the distance from A to B; moving B to the right shortens the distance from B to C.

76.322 inches appears to be the optimal result, with two in the back corners and the third in the center of the front.

Last edited by: ThatDonGuy on Apr 19, 2020
Wizard
Joined: Oct 14, 2009
• Posts: 22825
April 19th, 2020 at 7:24:05 PM permalink
Quote: billryan

Who pushes the button ?
In NYC, many places have what we call "Jewish" elevators. On the Sabbath, some Jews are not allowed tp use phones or push a button and the elevators are programmed to stop o every floor.

Doesn't getting into the elevator at all cause it to consume more electricity? I thought the spirit of the Sabbath rules were shun modern conveniences and not consume power.
It's not whether you win or lose; it's whether or not you had a good bet.
jjjoooggg
Joined: Jul 13, 2012
• Posts: 963
April 19th, 2020 at 7:27:21 PM permalink
To limit sharing air, each occupant would walk to an empty corner and face the corner.

But if they are wearing masks. It would be more important to not bump into someone.
Besides study abroad. Born and lived in Tx my whole life.
Mosca
Joined: Dec 14, 2009
• Posts: 3813
April 19th, 2020 at 8:10:25 PM permalink
Quote: ThatDonGuy

It's probably like the elevators at Thed - er, The D - where you select a floor before you get in the elevator.

Let A be in the back left corner, B be in the back right corner, and C be in front, halfway between the two sides.
A and B are 80 inches apart; A and C are sqrt(652 + 402) = 76.322 inches apart, as are B and C.
If, say, C moves forward, then the distance from B to C is less than 76.322, unless C moves to the left, but this would make the distance from A to C less than 76.322.
Therefore, any solution requires that A and B be in the back somewhere.
Suppose B moves to the center of the back. The maximum distance from B to C that would be less than the distance from A to C is 76.322, when B is in the front right corner, but the distance from A to B is only 40.
Moving B to the left shortens the distance from A to B; moving B to the right shortens the distance from B to C.

76.322 inches appears to be the optimal result, with two in the back corners and the third in the center of the front.

Wouldn't it still have to be an equilateral triangle? A in the far left corner. B in the far right corner. C in the front. Then they adjust so that they are equidistant from each other, along the walls to maximize the triangle. B would move forward a little, along the wall, increasing his distance from A, C would move a little to his left. Also, they enter and leave in reverse order. A goes to a corner first, leaves last. Then B, then C. But again, the answer has to be an equilateral triangle.
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FleaStiff
Joined: Oct 19, 2009