# Rainy day

1. Mar 20, 2005

### T@P

there is a three story building, with a total of 12 people in it. it rained. and the roof leaked.

the people from the third floor asked the second floor people if they could go down to the second floor. the second floor people then said they could only acomodate (on the second floor) the same number of people as there are already on it.

it rained more

the people from the second floor (together with the first floor refugees) asked the first floor people of they could go down to the first floor. they did the same thing the second floor people did: the number of people that can go down onto the first floor must be equal to the number of people that are on the first floor already.

if there were an equal number of people on all the floors after the changes, what was the original arrangement?

just for clarification: not everyone moves down a floor. some people have to stay on the higher floors even though its leaking there. also, there is the boring and the amazingly easy way to do the problem. not that its that hard anyway, but theres just an easier way

2. Mar 20, 2005

### bjr_jyd15

should that be 3rd flr?

3. Mar 20, 2005

### BicycleTree

Answer: 4 people on floor 1 at the end, so move half of them back to floor 2 to undo the move down to floor 1. Then that's 6 people on floor 2 and 2 people on floor 1. Now move half of floor 2 to floor 3 to undo the move down to floor 2. So originally there were 2, 3, and 7 on floors 1, 2, and 3 respectively.

4. Mar 20, 2005

### Gale

here's what i did: x is the number originally on the bottom floor. At the end, the number on the bottom floor is 2x. the number on the bottom floor at the end must equal the number on the other floors, and the sum of them all equals 12. So, 2x(3) also equals 12. 12=6x. x=2. then solve backwards from there to get that originally 7 were up top, 3 in the middle, and 2 at the bottom.

5. Mar 20, 2005

### T@P

sorry bjr, but i think its right as it is. and ya i did it bycicle tree's way, but i guess your way works too gale17

its all about going backwards. 4/2 = 2
2 + 4 = 6
6/2 = 3
4 + 3 = 7

then make sure you did nothing stupid ;)