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Cows, horses and dogs (Posted on 2008-10-20) Difficulty: 2 of 5
I have cows, horses and dogs, a different prime number of each. If I multiply the number of cows (c) by the total of cows and horses (c+h), the product is 120 more than the number of dogs (d), that is: c*(c+h) = 120 + d.

How many of each do I have?

  Submitted by pcbouhid    
Rating: 4.0000 (1 votes)
Solution: (Hide)
The equation c*(c + h) = 120 + d reveals that d cannot equal 2, the only even prime number, since C would then also have to be 2, which is not a different number.

So d must be odd, from which either c or h must equal 2, since the sum of the two would otherwise be even.

Clearly, h must then must be 2, since c equals 2 would made the product even. Rewriting the equation, we get:

c2 + 2c - 120 = d
(c + 12)(c - 10) = d

(c - 10) must equal unity in order for d to be a prime. Then:

c = 11, h = 2 and d = 23 is the unique solution.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
No SubjectAmanda Holmes2022-04-18 11:11:02
SolutionPuzzle SolutionK Sengupta2008-11-21 05:05:24
AnswerK Sengupta2008-11-20 00:41:13
SolutionSolutionhoodat2008-10-26 23:51:19
re: proof of uniquenesspcbouhid2008-10-21 07:39:21
Solutionproof of uniquenessPaul2008-10-20 21:01:56
re(2): Agreed - to rodpcbouhid2008-10-20 17:55:32
re: Agreedrod hines2008-10-20 17:18:19
Agreeded bottemiller2008-10-20 16:38:48
re: Odds arerod hines2008-10-20 15:14:16
Odds areed bottemiller2008-10-20 13:25:15
Solutioncomputer solutionCharlie2008-10-20 12:22:28
Solutioned bottemiller2008-10-20 11:23:11
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