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100 Herbivores (Posted on 2002-06-10) Difficulty: 2 of 5
There are a total of 100 animals: cows, sheep and buffaloes. These 100 animals ate 100 bunches of grass.

Every cow ate 5 bunches, every buffalo ate 3 bunches and every sheep ate only 1/3 bunch.

How many cow, sheep and buffalo are there? You only know that there is at least one of every kind of animal.

See The Solution Submitted by vohonam    
Rating: 2.5455 (11 votes)

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Some Thoughts Some Thoughts Comment 9 of 9 |
(In reply to Puzzle Solution by K Sengupta)

Having regard to the given conditions, this problem has three different solutions given by:

(#cows, # buffaloes, # sheep) = (4, 18, 78); (8, 11, 81) ; (12, 4, 84)

Interestingly, the number of cows in each of these solutions is a multiple of 4, the number of sheep in each of these solutions is a multiple of 3. In addition, the respective total count of buffaloes in two of these solutions are 4 and 18 (both composite numbers), while in the remaining solution the said count is 11, a prime number.

Accordingly, if we impose the restriction that the number of buffaloes must correspond to a prime number, then we have only one solution, that is:

(#cows, # buffaloes, # sheep) = (8, 11, 81)   

 

Edited on November 6, 2007, 4:24 am
  Posted by K Sengupta on 2007-11-06 04:23:36

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