You have 4 weights weighing 2,3,5 and 7 pounds. The problem is none of them are marked. What is the fewest number of weighings you need using a balance scale figure out which weights are which?
I could do no better than five weighings. (I considered weighing 2 against 2 weight combinations, but that didn't seem to lead anywhere, due to my want of ingenuity).
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Call the four weights a,b,c,d.
The possibilities are:
abcd abdc acbd acdb adbc adcb bacd badc bcad bcda bdac bdca
cabd cadb cbad cbda cdab cdba dabc dacb dbac dbca dcab dcba
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First two weighings:
Weigh a against b, then weigh c against d.
Let's say that a<b and c<d.
This leaves:
abcd acbd acdb cabd cadb cdab
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Next two weighings:
Weigh a against c, then weigh b against d.
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If a<b, c<d, a<c, b<d:
The possibilities are:
abcd acbd
One more weighing is needed:
Weigh b against c
Five total weighings.
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If a<b, c<d, a<c, b>d:
The only possibility is:
acdb
Four total weighings.
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If a<b, c<d, a>c, b<d:
The possibilities are:
abcd acbd
One more weighing is necessary: b against c.
Five total weighings.
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If a<b, c<d, a>c, b>d:
The possibilities are:
cadb cdab
One more weighing is necessary: a against d
Five total weighings
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Posted by Penny
on 2004-07-25 12:07:26 |
A non-computerized finish
