A farmer buys 100 animals for exactly 100 coins. - Each buffalo costs 10 coins.
- Each pig costs 3 coins.
- Each chicken costs 1/2 coin. How many animals of each type can you buy?
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The Chinese Farmer's Riddle
The Chinese Farmer's Riddle comes from the tradition of well-told problems: a simple framework, a clear difficulty and a solution that seems almost obvious when it has already been seen.
Hints
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- There is no need to blindly try combinations: first translate it into quantity and cost equations.
- Since chickens cost half, the natural thing is to eliminate decimals by multiplying by 2.
- Afterwards, the most expensive variable is very restricted and the system practically closes down.
Solution
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Answer: He bought 5 buffaloes, 1 pig and 94 chickens. Explanation: Let $b$ be the number of buffaloes, $c$ be the number of pigs and $p$ be the number of chickens. So:
$$ b+c+p=100 $$
and
$$ 10b+3c+0.5p=100. $$ Multiplying the second equation by 2: $$
20b+6c+p=200.
$$ Subtracting the first:
$$ 19b+5c=100. $$ Testing positive integer values, the only solution is $$
b=5,\quad c=1,\quad p=94.
$$ It meets both the total number of animals and the total cost.
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