20040510, 14:11  #1 
Aug 2003
Upstate NY, USA
2×163 Posts 
buckets of water
The problem is that we have 3 buckets of water.
Bucket 1 has a capacity of 3 gallons and is initially empty. Bucket 2 has a capacity of 5 gallons and is initially full of 50 degree water. Bucket 3 has a capacity of 6 gallons and is initially full of 90 degree water. Now the "nonreallife" conditions: 1) We can only move water between these three buckets. 2) We can purposely spill water, but once it's spilled we can't pick it back up. (so don't try this inside your home) 3) The water temperature will not change due to air temperature, change in pressure, etc. 4) When you mix water from buckets of different temperature, all the water becomes the average temperature before our next transfer. (no waiting for heat transfer  mixing 1 gallon of 50deg and 3 gallons of 90deg produces 4 gallons of 80deg) 5) We can only be precise when completely filling or emptying a bucket (i.e. pouring 3 gallons from the 6 gallon bucket into the empty 3 gallon bucket) The puzzle is what integer temperatures between 50 and 90 can be produced? This is not my puzzle, so I only have a partial answer. HA! You thought this would be my partial answer, didn't you? Also, this is the first puzzle I've posted so if anything seems unclear, let me know. 
20040510, 14:57  #2 
Jun 2003
The Texas Hill Country
3^{2}×11^{2} Posts 
A small question about mixing:
Consider the following  The 5 gal bucket is full. What happens if we attempt to pour the contents of the 6 gal bucket into it? Obviously, we will spill 6 gal. But at what temperature? Do we assume that there is absolutely no mixing (The original 5 gal @ 50 degrees remains in the bucket and the 6 gal @ 90 degrees gets spilled) ? or this  Pour out 3 gal of 90 degree water. The remaining water has an average temperature of (5*50 + 3*90)/8 = 65 degrees. Unfortunately, none of the water is at that temperature. However, we can mix the water in the 3 buckets a (infinite) number of times and get it all to the same temperature. Is the procedure allowed? 
20040510, 16:54  #3  
Aug 2003
Upstate NY, USA
2×163 Posts 
Quote:
Quote:


20040514, 20:51  #4 
Aug 2003
Snicker, AL
1677_{8} Posts 
An interesting problem. Lets say I pour 3 gallons of 90 degree water into the 3 gallon bucket. I then pour 3 gallons of 50 degree water back into the 6 gallon bucket producing a temperature of 70. Now I have 3 temperatures to work with.
3 gallons (in 3 gallon bucket) at 90 2 gallons (in 5 gallon bucket) at 50 6 gallons (in 6 gallon bucket) at 70 It looks like a simple recursive from there. Fusion 
20040514, 20:58  #5  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2^{2}×23×109 Posts 
Quote:
or Pour 3G of 70D from 6GB into 5GB, get 5G of 72D Total accounted for 50, 70, 72, 74, 90. 

20040515, 10:43  #6  
May 2004
2^{2} Posts 
Quote:
Bucket 1 has a capacity of 3 gallons and is initially empty. Bucket 2 has a capacity of 5 gallons and is initially full of 50 degree water. Bucket 3 has a capacity of 6 gallons and is initially full of 90 degree water. Meaning that the following is not allowed: Pour 1 gallon of water from Bucket 2 into Bucket 1. If this true, I believe I have the answer. I'm going to try to work with it a little more to see if I've exhausted every permutation. 

20040515, 12:17  #7  
Jun 2003
The Texas Hill Country
10001000001_{2} Posts 
Quote:


20040515, 14:55  #8 
Aug 2003
Upstate NY, USA
2·163 Posts 
Right  the only initial actions that can be made are to:
A) Pour 3 gallons from bucket 2 into bucket 1 B) Pour 3 gallons from bucket 3 into bucket 1 
20040515, 17:36  #9  
Jun 2003
The Texas Hill Country
3^{2}·11^{2} Posts 
Quote:
C) Pour 5 gallons from bucket 2 onto the floor D) Pour 6 gallons from bucket 3 onto the floor (But they don't lead to any interesting possibilities.) 

20040515, 17:41  #10 
Aug 2003
Upstate NY, USA
2×163 Posts 
I found those trivial .... and thus of no interest to people here

20040515, 20:20  #11 
May 2004
4_{8} Posts 
I'm still trying to think of some options, but I've been able to account for the following temperatures.
50, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 90 I'm still not sure whether or not the integer temperatures would follow a difference to 50 and 90 pattern. If so, notice peculiarities would be 54, 59 All of these temperatures are attainable in a discrete number of steps. I don't believe using an infinite number of steps would result in anything worthwhile. 
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