Goldfish Student Child

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  Need help with riddle?
  

  One hundred children had a chance to win 1 to 4 fish at a school carnival. By the end of the day, 77 won goldfish, 83 won angel fish, 56 won zebra fish, and 85 won carp. All 100 children were eligible for each drawing, and each won at least 1 fish. How many students won all 4 kinds of fish? Keep in mind that this number is the least number of students who won all 4 fish for certain.

  The Answer:

  14.

  Hang on.
  Assuming that you could only win ONE TYPE of fish and not multiple types:

  What you do is you see how many kids didn’t win a certain type of fish. For example, if 77 children won a goldfish, then this obviously means that 23 children did not. Therefore, for sure 23 children did not win all 4 kinds of fish. Using common sense, you deduce that the number of children who didn’t win all 4 kinds of fish would have to be at the least the highest number of those who didn’t win a specific type.
  For example, 56 children won zebra fish, therefore 44 surely didn’t win all 4 kinds. Does this automatically mean that 56 children won all 4 kinds of fish?? Not really.
  You have to remember that each child had a chance of winning 4 fish. Therefore there had to have been a total of 400 fish. (100×4=400). But in the results we see that only 301 fish were won. (77+83+56+85=301). So what you do now is add the rest of the number of fish that were won (not including 56 because this is the number you THINK may have won all 4 kinds of fish.)
  So you add 77+83+85= 245.
  Remember that a total of 301 fish were given out.
  So subtract 301-245= 56 (The number of children who won zebra fish.)
  Now if 56 were your answer then you would have to multiply it by 4 (because you are stating that 56 people won all 4 kinds of fish) 56×4=224
  You don’t want to do this because you want to make sure that what you get (224) plus the total of the other fishes won (245) adds up to 301. But 224+245= 469. This wouldn’t work.

  So since you are being asked how many students won ALL 4 kinds of fish, you see how many kids could win without going over 56. Easiest way to do this? Divide 56 by 4. 56/4= 14.

  So 14 children won all 4 kinds of fish.

  
  
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  June 18th, 2009 | admin | No Comments | Tags: care, guide, health, tax, tips