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To Find the Heavy Marble, Divide and Conquer Asymmetrically

Date: 01/14/2011 at 15:54:13
From: Dawn
Subject: find the heaviest marble of eight in two weighings

There are eight marbles of the exact same size and color. One of the eight
is slightly heavier than the other seven.

With a balance scale, how do I find the heavier marble in just TWO
weighings?

By weighing four and four, I can eliminate it down to two and two; and on
the third weighing, to one and one -- but to eliminate seven or six in the
first weighing is boggling my mind.

So I can solve this easily in three weighings; but ... two?



Date: 01/14/2011 at 15:59:08
From: Doctor Ali
Subject: Re: find the heaviest marble of eight in two weighings

Hi Dawn!

Thanks for writing to Dr. Math.

We can set aside two of the marbles and put the remaining six on the
scale -- three in one pan, three in the other.

If they had equal weights, it would mean that the heavier marble is among
the two marbles that weren't on the scale. But if one side goes down, then
we know that the heavy marble is among those three. In that case, we set
aside one of those and put the remaining two of those three on the
scale....

Can you take it from here yourself?

Please write back if you still have any difficulties.

- Doctor Ali, The Math Forum
  http://mathforum.org/dr.math/ 



Date: 01/14/2011 at 23:53:24
From: Dawn
Subject: Thank you (find the heaviest marble of eight in two weighings)

Thank You!

This was a bit like the one about the three story brick building with no
windows, three light switches at the bottom of the first floor, and you
get one chance to go upstairs one time, without a time limit -- but you
must figure out in that one trip which light switch works the light bulb
on the third floor :) If only I hadn't been traveling for two days before
this question....

But thank you so much! I love smart people! Will check in again if I get
stumped. 

Dawn
Associated Topics:
Middle School Logic
Middle School Puzzles

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