having 10 cigarette packets.9 packets having 10 gram cigarettes but in 1 packet 11 gram cigarettes are there.we are having digital weighing machine and need to weigh only one time.how to find which packet is having 11 gram cigaretts??

• My Solution:
  Suppose that each packet has 10 cigarettes. First step: Take from the first packet one cigarette, 2 from the second, 3 from the third....10 from the 10th packet. Now we have: 1+2+3+4+5+6+7+8+9+10= 55 cigarettes to weigh. Second step: Use the digital weighing machine to get their weight. Result discussion: If the packets have equal weights of 10 grams each then the total resulting weight would be 55 grams but since we have one packet with an excess weight ratio of 0.01 grams per cigarette then we can find out from this ratio exactly which packet has the 11 grams weight. For example if the total weight for these cigarettes is 55.03 then the third packet is the one we are looking for since we took from it (3 x 0.01 =0.03 grams) which is exactly the additional weight we got (55.03 - 55= 0.03 grams).
• 8 years agoHelpfull: Yes(4) No(1)
• put the 10 cigarette packets one by one in machine.
  it will be increasing by 10 ( 10..20..30..like that)
  if we get weight that end with 1(like 11 or 21 ...like that)
  stop there.
  the last packet that u put is 11 gram packet
• 9 years agoHelpfull: Yes(3) No(5)
• ram , the question says - u can weight only 1 time :)
• 9 years agoHelpfull: Yes(0) No(0)