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Flowers (Posted on 2003-03-01) Difficulty: 1 of 5
How many flowers do I have if all of them are roses except two, all of them are tulips except two, and all of them are daisies except two?

See The Solution Submitted by Ravi Raja    
Rating: 2.9231 (13 votes)

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Solution Solution To The Second Interpretation | Comment 17 of 19 |
(In reply to Solution To The First Interpretation by K Sengupta)

Let us consider the second interpretation, where There exists at least one flower in the given collection other than Rose, Tulip or Daisy.

Let the total number of flowers that are different from roses, tulips and daisies be n.

If n>=3, then subtracting 2, we will always have at least one flower in the collection that is different from rose, tulip or daisy. This contravenes all the three given conditions.

Now, by the given conditions, it follows that the respective number of roses(r), tulips(t) and daisies(d) are equal.

If n=1, then r=t=d=0, results in a violation of the given conditions. Similarly, r=t=d>=1,  causes similar contravention of the given condition.

If n=2, then it is readily observed that r=t=d>=1 causes violation of the given conditions, while r=t=d=0 is in conformity with all the given conditions.

Accordingly, the total nuber of flowers in the collection is 2, and:

Number of Roses = 0
Number of Tulips = 0
Number of Daisies = 0
Number of flowers that does not correspond to Rose, Tulip or Daisy = 2

Edited on March 11, 2008, 11:12 am
  Posted by K Sengupta on 2008-03-11 10:58:05

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