Elevator Puzzle
December 11, 2008 3 Comments
I made up a puzzle. It may already exist in some form (there are many possible ways to arrange a puzzle based on the same sort of idea) but I made it up independently. I may not have ironed out all the kinks but still I figured my 1.01 daily readers might wish to try their hand at it. I’m going to try to state it in a way where you get just the information you need and no more. I can’t tell how hard or easy this puzzle is (yet), perhaps because it is based on real events and so I’m too close to it. You have to answer all the questions about the situation, and give reasons why. Without further ado:
Puzzle
Adam, Bill, Chad, Dave, Eric and Frank are riding up an elevator, having all entered on the ground floor. The buttons for floors 2, 3, 4, 6, 7 and 11 are lit up. It stops on 2 and Dave and Eric get out. Bill then gets mad at someone (sighs). Chad smiles at Adam. Frank gets out on 3. I will also tell you that someone gets out on 7.
Questions:
1. Who did Bill get mad at? Why?
2. What floor was Bill going to?
3. You know at least one person got in the elevator before Bill. Why, and who?
4. You also know someone that got in the elevator before the person from question 3. Who?
5. Someone felt embarrassed. Who?
6. Who (if anyone) got off on 4?
7. Who (if anyone) got off on 6?
8. Who got off on 7? (I told you someone did)
9. Why didn’t Chad get mad?
10. Did Adam get mad?
11. What floor did Adam go to?
12. All six people entered the elevator in time to make it to their respective desks at exactly 9:00. Two people ended up being a bit late, however. Who?
13. Bill knows the floors that at least two other people in this elevator work on. Which two? There’s at least one other person in the elevator whose floor Bill didn’t know (till this ride). There are two people that person could be. Which two?
Bonus Question: By regulation, there are two legal types of elevators in this city. Type I has the floor-buttons in two vertical columns spaced 12 inches apart. Type II has the buttons all in one vertical column. Which Type is this elevator?
Well, that should be enough questions. I think if you get the basic idea you’ll get most of the questions. I wonder how many you could get without getting the basic idea, but just from how I phrased it. Probably some. If so, the puzzle needs tuning up a bit. I guess I’ll find out (if anyone comments, that is).
I’ll post the answers (or at least, my answers) a bit later on.
SOLUTION
I’ll assume no takers and post the solution (or my solution, anyway). The basic key to the answer:
Adam works on floor 7 but accidentally pressed 6 first.
How do we know? The setup starts with six people in the elevator and six buttons pressed. But two people get off on 2 – now there’s 5 floors pressed but only four people. Most likely someone pressed more than one button (it’s also possible that i.e. someone pressed one button but changed his mind and got off on a floor someone else pressed, but this is a ‘most likely’ sort of puzzle). After Frank gets out on 3, there are three people left on the elevator (Adam, Bill and Chad) and four floors to go (4,6,7,11). Bill gets mad at someone when he figures out someone pressed two buttons, so most likely he’s the person most inconvenienced by this: he’s going to 11. Chad smiles at Adam so he’s not inconvienced by the double-push: he’s going to 4 and will get off anyway. Clearly Adam pressed both 6 and 7. I told you someone gets off at 7 so that’s Adam.
These are my answers then:
1. Who did Bill get mad at? Why?
Bill got mad at Adam cuz he pressed two buttons, making Bill’s trip to 11 longer.
2. What floor was Bill going to?
11.
3. You know at least one person got in the elevator before Bill. Why, and who?
Adam must have gotten in the elevator prior to Bill. If he hadn’t, Bill would’ve seen Adam press the two buttons and been annoyed by him right away. But Bill only got mad after two people got out on 2; i.e., he only realized someone pressed two buttons (which wasn’t obvious initially, when there were 6 people and 6 buttons pressed) after two people got out on the same floor.
4. You also know someone that got in the elevator before the person from question 3. Who?
Chad got in before Adam, and saw him press the two buttons. That’s why he was smiling at Adam when Bill got annoyed; Chad knew Adam was the culprit.
5. Someone felt embarrassed. Who?
Adam, obviously.
6. Who (if anyone) got off on 4?
Chad got off on 4. The double-push didn’t affect him so he found the whole thing amusing.
7. Who (if anyone) got off on 6?
Nobody. We know someone got off on 7 and that was Adam.
8. Who got off on 7? (I told you someone did)
Adam.
9. Why didn’t Chad get mad?
Because a double-push above his floor doesn’t delay him at all.
10. Did Adam get mad?
No. He was the culprit.
11. What floor did Adam go to?
7.
12. All six people entered the elevator in time to make it to their respective desks at exactly 9:00. Two people ended up being a bit late, however. Who?
Adam and Bill were late, because they both work above 6, where the elevator stopped by accident.
13. Bill knows the floors that at least two other people in this elevator work on. Which two? There’s at least one other person in the elevator whose floor Bill didn’t know (till this ride). There are two people that person could be. Which two?
He must know that Chad works on 4 and Frank works on 3. Otherwise, when Dave and Eric left, he wouldn’t have known who to blame for pressing 6-7. Meanwhile, he didn’t know that Dave and Eric both work on 2 (he might have known one of them did). If he had, he’d have figured out the double-push from the get-go instead of only after they both got out on 2.
Bonus Question: By regulation, there are two legal types of elevators in this city. Type I has the floor-buttons in two vertical columns spaced 12 inches apart. Type II has the buttons all in one vertical column. Which Type is this elevator?
Type II. Accidentally pushing 6 instead of 7 wouldn’t be likely with a two-column 12-inch separation layout, because assuming the numbers were arranged left-to-right, 6 and 7 would end up in different columns and accidentally pushing one when you meant to hit the other just wouldn’t happen.
Well, I was waiting for your – and others’ input, thinking I might have completely different reasoning – and I do.
1st, if someone gets’mad in the elevator because someone else’s pressed the wrong button, this person should be hospitalized pronto: he’s a walking postal worker’ bomb waiting to explode. At the most, people get annoyed in these situations.
2nd, my reason to get annoyed would be if I were going to the 11th floor and someone needed to hold up an elevator because they are too lazy to get to the second. And if that is actually TWO people, I’d be annoyed twice as much. Actually, that what’s happening every morning in my office building. Except when the cab is full of passengers , and it’s 2 min to 9am, and we all are going to the top floors and 2 lazy asses are getting off on Second – there is a collective *eyeroll*, and sometime more than that.
So you can see how the whole reasoning could sverve off right from that point…
Yes. Both your points are good, actually. They illustrate how these types of puzzles can be ‘cultural’. Your elevator experience is different from mine so you interpreted things differently.
In particular your point #2 made sense for a building I used to work in and indeed I did get annoyed by people taking the elevator to 2. What has changed re: my current (bigger) building is that stairs (even to 2) aren’t a very good option (the first floor/lobby is very tall) so I don’t get annoyed by people taking the elevators even to 2. But to remove this factor either way, my puzzle could therefore be improved by changing the numbers to (say) 4,5,6, 8,9 and 11.
Re: #1, well when I said ‘mad’ I didn’t really mean MAD, just annoyed, like you say. So I agree that would be a better way to phrase the puzzle. It’s a work in progress
Thanks,
glad to be of service to Puzzle World