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# Elevator

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Posted 10 July 2007 - 05:25 AM

A clever mischief-maker rewired an elevator in an eight-floor office building (seven numbered upper floors plus the basement). The result is that when the elevator is on the basement level - which corresponds to the B button in the elevator - pressing the button to go to the desired floor does not necessarily get one there. Three of the seven buttons work correctly; two take one to a floor with a number twice that of the floor to which they should; and two take on to a floor with a number half that of the floor to which they should. The button marked 1 for the first floor (next level above the basement) does not work correctly. There is a way to get to every floor by pushing just one button; the rewiring was done so that each button does get one to a different one of the seven floors. How is the elevator wired? That is, what is the result of pushing each of the seven buttons?
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### #2 normdeplume

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Posted 10 July 2007 - 10:05 AM

Button Floor
B --------B
1 --------2 (x2)
2 --------1 (1/2)
3 --------6 (x2)
4 --------4 OK
5 --------5 (OK)
6 --------3 (1/2)
7 --------7 (0K)
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### #3 someids

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Posted 29 January 2008 - 07:29 AM

Button 1 does not work correctly -> It will lead to 1/2 floor or 2nd floor. Must be 2nd floor.
Therefore button 2 does not work correctly -> It will lead to 1st floor or 4th floor. If it does not lead to 1st floor, no other button can. Must be 1st floor.
If so, how do we get to 4th floor? Can not be from button 2, cannot be from button 8 (no such button). It must be from button 4.
Out of 3 even button 2,4,6, button 4 works correctly, hence button 6 must lead to 3rd floor.
Therefore button 3 does not work correctly -> It will lead to 6th floor.
We come to the solution drawn by normdeplume.
Nice puzzle, thanks

Edited by someids, 29 January 2008 - 07:31 AM.

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### #4 SpelChexRool

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Posted 06 March 2008 - 03:48 AM

Actually, unless I have misread the solution, normdeplume's submission results in 4 correct floors (B, 4, 5, 7), not 3 as required by the author. One that might be a better fit would be:

8 -- 4 (x0.5)
7 -- 1 (simple mismatch)
6 -- 3 (x0.5)
5 -- 5 (OK)
4 -- 8 (x2.0)
3 -- 6 (x2.0)
2 -- 2 (OK)
1 -- 7 (simple mismatch)
B -- B (OK)

This solution also has the added benefit of being rather symmetrical (if that appeals to you...) since doubles and halves line up nicely.

Button 1 does not work correctly -> It will lead to 1/2 floor or 2nd floor. Must be 2nd floor.
Therefore button 2 does not work correctly -> It will lead to 1st floor or 4th floor. If it does not lead to 1st floor, no other button can. Must be 1st floor.
If so, how do we get to 4th floor? Can not be from button 2, cannot be from button 8 (no such button). It must be from button 4.
Out of 3 even button 2,4,6, button 4 works correctly, hence button 6 must lead to 3rd floor.
Therefore button 3 does not work correctly -> It will lead to 6th floor.
We come to the solution drawn by normdeplume.
Nice puzzle, thanks

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### #5 bonanova

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Posted 06 March 2008 - 10:18 AM

Actually, unless I have misread the solution, normdeplume's submission results in 4 correct floors (B, 4, 5, 7), not 3 as required by the author.

A closer reading of the OP reveals that ...

The result is that when the elevator is on the basement level - which corresponds to the B button in the elevator - pressing the button to go to the desired floor does not necessarily get one there. Three [4,5,7] of the seven [1,2,3,4,5,6,7] buttons work correctly;...

... normdeplume's answer does meet the criteria.
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Vidi vici veni.

### #6 isolveall

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Posted 02 April 2008 - 10:19 AM

WHY WE NEED TO GET INTO LOGIC OR MATHS TO SOLVE THIS PROBLEM?
IT IS INDICATED THAT WHEN ELEVATOR IS AT BASEMENT LEVEL THE SWITCHES DOES NOT WORK PROPERLY

THIS MEANS AT ALL OTHER LEVELS THEY WILL WORK PROPERLY.

YOU MAY PRESS ANY BUTTON AT BASEMENT LEVEL TO TAKE AT ANY OTHER LEVEL AND ALL JOURNEY FROM THAT LEVEL WILL TAKE YOU TO CORRECT LEVEL!!!
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Posted 11 June 2008 - 03:32 PM

I got what normdeplume got. Firstly I saw that we were on the basement so it was out of 1,2,3,4,5,6,7. Since 1 does not work correctly, it must be that 1 leads to 2 as 1 x 2 = 2 and vice versa so 2 leads to 1. The only other pair which can be manipulated in this way is 3 and 6, so 3 leads to 6 and 6 leads to 3. Another pair is 2 and 4, but since 1 doesn't work correctly, and so must lead to 2 and 2 to 1, 4 can't also lead to 2 since they must all go to different floors. So at the end you get what normdeplume said. where 1 --- 2, 2 ---- 1, 3 --- 6, 4 OKAY, 5 OKAY, 6 ---3, 7 OKAY!!

COOL PUZZLE!!
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### #8 preflop

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Posted 22 August 2008 - 09:02 PM

1-2 (double)
2-1 (half)
3-6 (double)
4-4 (ok)
5-5 (ok)
6-3 (half)
7-7 (ok)

B is irrelevant because we are in the basement and it is a letter and so 2x and 1/2 cannot be applied to it.
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Sent from my rotary dial phone.

### #9 lenzvlt

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Posted 05 November 2011 - 03:06 PM

1st floor button to 2nd Floor (1x2)
2nd floor button to 4th floor
4th floor button to 2nd floor

Basement, 3rd, 5th, 6th, 7th floor correct
NECESSARILY IS KEY HERE-not positivly

Edited by lenzvlt, 05 November 2011 - 03:07 PM.

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Posted 06 November 2011 - 09:03 AM

WHY WE NEED TO GET INTO LOGIC OR MATHS TO SOLVE THIS PROBLEM?
IT IS INDICATED THAT WHEN ELEVATOR IS AT BASEMENT LEVEL THE SWITCHES DOES NOT WORK PROPERLY

THIS MEANS AT ALL OTHER LEVELS THEY WILL WORK PROPERLY.

YOU MAY PRESS ANY BUTTON AT BASEMENT LEVEL TO TAKE AT ANY OTHER LEVEL AND ALL JOURNEY FROM THAT LEVEL WILL TAKE YOU TO CORRECT LEVEL!!!

CAPS LOCK IS HOW YOU KNOW I'M SERIOUS!
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