Word Puzzle ( yet another thread)
Wednesday, January 14, 2004 by Rocky Nimda | Discussion: WinCustomize Talk
The Problem: You have a set of Balance Scales like the one shown here:
You have 9 identical looking marbles. You can't tell the difference between any of the 9 marbles by looking at them.
One of the 9 marbles is ever so slightly denser than the others (thus it weighs more). The only way to find out which marble is the one that is denser is to use the balance scales.
One way to do this would be to put 1 marble on one side and 1 marble on the other. If one was heavier than the other, you would then know which of the nine was the heaviest. If they were the same, you could then take one of the marbles off the scales, and put another on. As you can see, this could take quite a few measurements. Worst case: too many to count.
Now, your task is to figure out how few measurements you can make to find the 1 dense marble.
Keep in mind; you can put more than 1 marble on each side of the scales at a time. Also, keep in mind the "worst case" for your solution. The solution I mentioned above could be solved in 1 measurement, but that's NOT worse case (it could take many more).
When you post your solution, don't just say I can find the dense marble with 6 measurements. You need to describe your solution. I have to be able to determine if the number of measurements you suggest is truly worst case or not.
By the way "6" is just used as an example here; it may or may not be the correct answer.
After this puzzle is solved, someone else could add another word puzzle to the thread.
You have 9 identical looking marbles. You can't tell the difference between any of the 9 marbles by looking at them.
One of the 9 marbles is ever so slightly denser than the others (thus it weighs more). The only way to find out which marble is the one that is denser is to use the balance scales.
One way to do this would be to put 1 marble on one side and 1 marble on the other. If one was heavier than the other, you would then know which of the nine was the heaviest. If they were the same, you could then take one of the marbles off the scales, and put another on. As you can see, this could take quite a few measurements. Worst case: too many to count.
Now, your task is to figure out how few measurements you can make to find the 1 dense marble.
Keep in mind; you can put more than 1 marble on each side of the scales at a time. Also, keep in mind the "worst case" for your solution. The solution I mentioned above could be solved in 1 measurement, but that's NOT worse case (it could take many more).
When you post your solution, don't just say I can find the dense marble with 6 measurements. You need to describe your solution. I have to be able to determine if the number of measurements you suggest is truly worst case or not.
By the way "6" is just used as an example here; it may or may not be the correct answer.
After this puzzle is solved, someone else could add another word puzzle to the thread.
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mrtee
Reply #22 Wednesday, January 14, 2004 9:50 PM
Reply #22 Wednesday, January 14, 2004 9:50 PM
You better mark the bags with the amount contained in each or you'll have to open it to look!
Ingui
Reply #23 Thursday, January 15, 2004 3:11 PM
Reply #23 Thursday, January 15, 2004 3:11 PM
yes you guys got it, sorry I didnt reply sooner. I got "called in" on Snow Duty. Your method seems to work but it's actually different, I think, than the answer I had. It is still 8 bags.
But the first even bags total $127 (1,2,4,8,16,32,64) the last bag is a $50 sac.
If the original total had been 12, you would end up with 4 bags(1,2,4 and 5)
the formula is : 2º, 2¹, 2², 2³, 2to the fourth, ... , 2 the sixth.
Anyway, seems we got a bunch o' einsteins here at WC
But the first even bags total $127 (1,2,4,8,16,32,64) the last bag is a $50 sac.
If the original total had been 12, you would end up with 4 bags(1,2,4 and 5)
the formula is : 2º, 2¹, 2², 2³, 2to the fourth, ... , 2 the sixth.
Anyway, seems we got a bunch o' einsteins here at WC
Corio
Reply #24 Thursday, January 15, 2004 6:19 PM
Reply #24 Thursday, January 15, 2004 6:19 PM
Awww....Was away for that one. Well, nobody pays what I say much attention here anyway... 
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Reply #21 Wednesday, January 14, 2004 9:15 PM