Give me a room

Logic Level 3

There are 1000 rooms in a row along a long corridor. Initially the first room contains 1000 people and the remaining rooms are empty. Each minute, the following happens: for each room containing more than one person, someone in that room decides it is too crowded and moves to the next room. All these movements are simultaneous (so nobody moves more than once within a minute). After one hour, how many different rooms will have people in them?

The answer is 31.

4 solutions

Abhijeet Verma
Jun 2, 2015

After 60 minutes, we will have 940 people in the first room, and 30 rooms with 2 persons each.

Bima Chandra
Aug 31, 2019

I found a neat pattern. It's a sequence such that the natural numbers from 2 are mapped to odd integers and for even terms of the sequence its the same as the odd term before it, so a 60 = a 59 . So a (2k-1) =k+1, a 59 =a_60 , 59=2*30-1, put in thirty you get 31 which is the answer.

Abin Das
Dec 9, 2015

After 1 min, the pattern will be 999 1

2 min 998 2

3 min 997 2 1

4 min 996 2 2

Hence at even minutes every room has even number of people with only the first room having more than 2 people.

After 60 min 940 2 2 2 ....... 2

which happens to be 30 rooms with 2 each and 1 room with 940 people. Hence total number of rooms occupied is 31.

Murlidhar Sharma
Jun 3, 2015

The number of filled rooms follow the series : $2,2,3,3,4,4.......$ So the answer is the 60th term in the series

Why? Can u explain?

Partho Kunda - 6 years ago

After the first min, 1 person is in room 2 and after the second min there are 2 people in room two. After the third min one person enters room 2 from room 1 and 1 person leaves room 2 to go to room 3. This continues and we get the series above.

(I thought it was obvious so did not explain it. But I should have)

Murlidhar Sharma - 6 years ago

Give me a room

The answer is 31.

4 solutions

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