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Counting Sheep (and Chickens) Solution

Genre: Math / Science Rating: 3 - Easy to Medium Source: Classic Puzzle 87
Brain Functions: Rational / Calculations Puzzle    Hint

A farmer has some (four-legged) sheep and some (two-legged) chickens. There are 30 animals in total. The total number of legs for these 30 animals is 84. How many animals of each kind are there?

This type of problem often frustrates people who dislike math, but it is really pretty simple. Start by pretending that the sheep are all standing on two legs instead of four. How many legs would the 30 animals have? Answer: 30 x 2 = 60. Subtract this number from the 84 legs that the problem calls for. Answer: 84 - 60 = 24. Every sheep is going to add 2 to the leg count, so we divide 24 by 2. Answer: 12 sheep. That means there are 30 - 12 = 18 chickens. Let's test our answer. Total leg count = 18 chickens x 2 + 12 sheep x 4. 36 + 48 = 84.



If you want a slightly tougher problem, read on. Imagine that exactly one of the thirty animals is a (leg-less) snake. Now how many of each animal are there?





There is 1 snake, so there are 29 other animals. If each has two legs, there would be 58 legs. Subtract 58 from 84 and get 26. Divide 26 by 2 to determine that there are 13 sheep. That means there are 16 chickens (30 - 1 - 13).



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