19 October 2005

Puzzling Wednesday

Four black cows and three white cows give as much milk in five days as three black cows and five white cows give in four days.

Which color cow gives more milk per day?

(Assume that the daily milk output of each cow is constant and the same for each black cow and each white cow.)

I will post the solution tomoorrow.

Slightly modified from puzzle #21 in C.R. Wylie, Jr., 101 Puzzles in Thought & Logic, Dover Publications, 1957.



Here is the solution.

Let B & W be the amount of milk/day given by each black & white cow, respectively.

The puzzle tells us that

5(4B + 3W) = 4(3B + 5W)

Rearranging & simplifying this gives

W=(8/5)B or W=1.6B

In other words, a white cow gives 1.6 times more milk/day than a black cow.

I can usually solve these types of puzzles only by using algebra. If you can think of a way to solve it without using algebra, please post it here.

Krauze said...

Easy. The group 4B+3W takes five days to produce as much milk as the group 3B+4W produces in four days. So if you want a group producing more milk, you exchange a black cow with a white cow. this means that the white cows produce the most milk.

PS. I've tried responding to your mail about Circus of the Spineless, but I get an automatic reply saying that I need to be approved to get around your spam wall, and I'm not sure if the system is accepting my submission.