This Week's Car Talk Puzzler
 

http://cartalk.com/content/puzzler/

You have a four-ounce glass, a nine-ounce glass, and endless supply of water. You can fill or dump either glass. What's the fewest number of steps in which you can measure six ounces?


I've spent about 15 minutes with this, but don't have an answer yet. Normally, I am pretty good at these "measure liquid in different glasses" puzzles (you can only make them so hard). I think that I am missing something easy.

Anyway, here it is, for those who want a crack at it. The answer won't be up until next week, but I imagine that someone will have this solved here within 10 minutes.

Dola--I have an answer, but I have to think that it can be done in less steps.

Hmm. Fill up the 4 oz 3 times, adding until you have a full 9 oz in the other. This will leave you with 3 oz in the 4oz glass from your last fill.

Dump out the 9 oz glass and pour the 3 oz in there. Now, fill up the 4 oz and add to the 9 oz. Fill the 4 oz again and fill the 9 oz to the top. This leaves 2 oz in the 4 oz. Dump the 2 oz into the 9 oz glass. Fill the 4 oz and add to the 2 oz in the 9 oz glass. Voila, 6 oz.

edit - I take it that was yours.

took me about 2 minutes, don't know if this is the shortest possible....


* spolier*

..
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fill 4 oz (4,0)
dump into 9 (0, 4)
fill 4 oz (4,4)
dump into 9 (0,8)
fill 4 (4, 8)
put 1 into 9 (3, 9)
dump 9oz out (3, 0)
pour 3 into 9 (0, 3)
fill 4 (4,3)
dump into 9 (0, 7)
fill 4 (4, 7)
put 2 into 9 (2, 9)
dump 9 (2,0)
pour 2 into 9 (0, 2)
fill 4 (4, 2)
pour into 9 (0, 6)
done! (16 steps)

Fill the 9
Dump 4 into the 4, leaving 5 in the 9
Dump the 4 out
Dump 4 into the 4, leaving 1 in the 9
Dump the 4 out
Dump the 1 from the 9 into the 4
Fill the 9 again
Dump 3 from the 9 to fill the 4, leaves 6 in the 9


Might not be the shortest method, but it works.

I was with you that far, but then I added a lot of extra steps. I had convinced myself that the only way to do it would be to get 1 oz. in the 4oz. glass and then dump the 9oz. into it.

Quik's halves the number of steps, so that's at least more correct, if not the best possible answer.