Simple math problems for recreation and research
"And yet the relation appears,
A small relation expanding like the shade
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Sunday, July 16, 2006
Weighing problem[S]
There are 101 coins among which one is counterfeit. we do not know whether the counterfeit coin is lighter or heavier ( than the rest of the coins ) which has to be determined within three weighings.how do you do it ?[S]
Time for solution. divide the coins into groups of 50+50+1 randomly.weigh, putting 50 coin group on one pan of the weighing machine and other 50 group on other pan. [i]if equal, then the left out coin is counterfiet.by comparing with any other coin we can find out whether the coin is lighter or else. [ii]if inequality:we can be sure coin is among one of the two fifty groups.( note that we cant determine anything now because we cant say inequality is caused due to lightness or heaviness and that is what we are ought to find ) now take the group of fifty that measured heavy(lighter) compared to other group.break a 50 group into two groups of 25 randomly and weigh them.if there is inequality we can deciede that counterfiet coin is here ( this group of 50) and it is heavy(lighter).else, it is light(heavy). I have tried to make solution as clear as possible.post a comment if you have any problem in understanding.
According to ur solution we'll hv to keep dividing the coins into groups till we find the counterfiet. But u hv mentioned that only 3 weighings are allowed. So can u make the solution a bit clearer?
5 comments:
counterfiet coin means a coin with weight different from rest in the group where rest of them have identical weight.
After you solve the problem check this out:
http://www.tutor.ms.unimelb.edu.au/coin/coin.html
Sudarshan
Time for solution.
divide the coins into groups of 50+50+1 randomly.weigh, putting 50 coin group on one pan of the weighing machine and other 50 group on other pan.
[i]if equal, then the left out coin is counterfiet.by comparing with any other coin we can find out whether the coin is lighter or else.
[ii]if inequality:we can be sure coin is among one of the two fifty groups.( note that we cant determine anything now because we cant say inequality is caused due to lightness or heaviness and that is what we are ought to find )
now take the group of fifty that measured heavy(lighter) compared to other group.break a 50 group into two groups of 25 randomly and weigh them.if there is inequality we can deciede that counterfiet coin is here ( this group of 50) and it is heavy(lighter).else, it is light(heavy).
I have tried to make solution as clear as possible.post a comment if you have any problem in understanding.
According to ur solution we'll hv to keep dividing the coins into groups till we find the counterfiet. But u hv mentioned that only 3 weighings are allowed. So can u make the solution a bit clearer?
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