Along a road lie an odd number of stones placed at intervals of 10 metres.These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man carried the job with one of the end stones by carrying them in succession. In carrying all the stones he covered a distance of 3 km. Find the number of stones
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"A man carried the job" should that be "a man started the job"? – Ross Millikan Jan 23 '14 at 05:50
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1"In carrying all the stones he covered a distance of 3 km" Is 3 km the distance that he walked since the start, or is that the distance he walked only with a rock in hand? – peterwhy Jan 23 '14 at 05:53
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@peterwhy: I read it as the total distance walked. It works out that way. – Ross Millikan Jan 23 '14 at 05:58
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This is not linear algebra. – Aditya Agarwal Sep 13 '15 at 10:26
3 Answers
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Let us measure in units of $10$ meters, so he goes $300$ units. If there are $n$ stones each side of center, he walks $n$ with the first stone, then $2(1+2+3+\dots (n-1))$ to collect all the stones on the side he started from, then $2(1+2+3+\dots n)$ to collect the ones on the other side. $n+n(n-1)+n(n+1)=300, (2n+25)(n-12)=0, n=12$ so there are $25$ stones total.
Ross Millikan
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For each of the $n-1$ stones between your starting stone and the middle stone, you have to walk from the middle stone to that stone, pick that stone up, walk back to the middle stone, and put that stone down. – peterwhy Jan 23 '14 at 06:14
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The answer is 25 stones. If you take 20(1+2+3..+12) you get 1560, which is the distanced traveled for one side of the center stone. Then you double it to get 3120, the total distance traveled for both sides. That is accounting for a trip from the center stone, to the desired stone, and back to the center stone. Since you start at one of the ends, you subtract 120 as you only have to make one trip to get that stone to the center, thus you traveled 3000 meters.
Riley
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But why did you do 20(1+2+3..+12) ?? I didnt understand this part... – Sudhanshu Jan 23 '14 at 06:06
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Sorry i edited my answer a little. It takes 20 meters multiplied by the index number of the stone from the center to get the total distance traveled to get that particular stone. The brute force way to go about doing it would be just starting at zero and adding up until you get around the desired answer, then fine tuning it when you get close. – Riley Jan 23 '14 at 06:10
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To clarify, from the center, if you are going to the fifth stone away, its 50 meters to the stone and 50 meters back to the center. Thats 5(10+10) or 5*20. Now you sum all of the stones 20(1+2+3+4+5....). – Riley Jan 23 '14 at 06:15
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its 301...3000meters/10 + 1(middle stone)
gaurav rajput
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I don't think so-he has lots of stones to carry and 3000 meters is the total walking distance. – Ross Millikan Jan 23 '14 at 05:51
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