Take a lift and guess the floor

Algebra Level 4

A lift was coming down stopping at each floor. A person in the lift was asked to guess the floor at every successive stop. The guesses made were in this order: 30, 23, 26, 29, 20, 28, 24, 21, 25, 27, and 22. If all the guesses except one were wrong, then which one was correct?


The answer is 27.

Rajen Kapur by Rajen Kapur , 72, India

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2 solutions

L N
Sep 26, 2014

Lol, brute force:

Pick a number, then count down from that number and see if your count down intercepts with another number on the list. Let's choose 23 for an example, then 23 -> 26, 22 -> 20, 21->29 20->20 Which is bad. Also, if no intercepts are found going down, then count upward, the only number that has no intercepts either direction is 27.

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plz sir can you give a clear solution i 'm kinda confused???

Palash Som - 6 years, 8 months ago

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@Palash Som Ok, let me see if I can elaborate: The basic idea is to check each number and see if that number is the ONLY solution. So let's start at 30, assume that is the only correct guess. Then at the next guess the elevator is at 29, which is not 23. So far so good. Now at the next guess the elevator has moved down one floor, and is at 28. The guess was 26, so far so good. If you repeat this process, you will see that when the guy guesses 24, the elevator must be at floor 24. But this would imply TWO correct guesses. Which is not what you want.

You also need to worry about previous stair too though. For example:

Now, what would happen if the guy's only correct guess was 25. This would not work, when the elevator is on floor 28, he also guesses 28.

If you do this for each number, the only number that satisfies being the only correct guess is 27.

L N - 6 years, 8 months ago

According to me, there is no rigorous way of solving this sum.If any solutions are there then it will be really tedious.I solved this sum using logic.This sum is not much related to algebra but is heavily weighed upon logic and reasoning.

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Just because it is based on logic and not algebra does not mean it cannot be proven rigorously. And what sum? There is no sum. The problem is related to classification of functions (I think), which is a big thing in algebra.

L N - 6 years, 8 months ago

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