I am wondering if I misread the verse.To the Ineffable All,
The answer is 972 cats. Here's why. You have to find out what number makes a perfect cube root of 3x/4. So x has to complete the cube and be divisible by 4. The first number that does that is 36. So three quarters of 36 is 27, which is a perfect cube. The second test is whether 3 times the number is a perfect square. Three times 36 is 108 which is not a perfect square, so the number 36 fails.
The next number that completes the cube and is divisible by 4 is 3x9x9x4 = 972 . Three quarters of 972 is 729, which is a perfect cube of 9. Three times 972 is 2916 which is a perfect square of 54. That proves that 972 is the smallest number that satisifies the conditions of the problem.
Ratch
I didn't claim originality and I didn't find it on the internet. The ditty is much much older than the net.Old but good question.
You used google, and didn't post before Ratch (or anybody... Welcome!)What do you mean "Well done Ratch"! It took him about 2 hours-It took me only 5 minutes.
http://www.dansmath.com/probofwk/probar18.html#anchor16413
After getting a "B" in College Algebra and an "A" in Precalculus last year (working on an ASEET), I hang my head in shame for not being able to do that.Ratch,
Thank you for explaining my answer, and as usual, you are right.
The way I reached that answer: x= # of cats, a and b are variables. x, a, and b are integers.
1) x = 1/3a^2
2) 3/4x = b^3
3) 4b^3 = a^2
I found solutions to equation #3 and tested them in equation #1. One can rule out certain values for "b" immediately by inspection and logic, like 4. I didn't consider primes for "b" because of equation #2. 8 was too similar to 4. It just seemed that "b" might be 9 or 12; although, I did try 6 too.
Once 9 was found to be viable for "b", the rest of the problem was solved.
John
True.thatoneguy "idiocy..." not at all you made a real attempt and came close.
If I were to say that you were the one to come closest to the answer-because studiot, Ratch (not saying they did but it is possible) and I found the answer on the net-would you still say "idiocy..." My point was to show that we can not compare ones knowledge, IQ etc because we are all on the net?
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by Jake Hertz
by Jake Hertz
by Jake Hertz