Let's say I've got two buckets, equal size. One is filled with water and the other with alcohol.
I take a cup of water out of the water bucket and pour it into the alcohol bucket. I mix it. I then take a cup of the mixture out of the alcohol bucket and pour it into the water bucket. Now, both buckets contain a mixture of water and alcohol.
Question:
1 - Is there more water in the alcohol bucket than there is alcohol in the water bucket, or is there more alcohol in the water bucket than there is water in the alcohol bucket?
2 - Are the percentages the same for both buckets?
Who wants to figure this one out?

well there is more alcohol in the water bucket.
adding water to alcohol the alcohol will absorb the water it will still be alcohol however in a more diluted state.
Adding alcohol to the water it will no longer be only water but a very dilute alcohol solution.
Thats what I think anyhow.
I am a fairly regular consumer of various dilutions of
alcohol so my thinking may be clouded

I'm sorry Tim. I don't follow your logic. Maybe you'd like to try again.

i would say there is more water in the alcohol bucket.

i hate pop quizes

I hated math when I was in school. Although intriguing, I don't like it any more since I've become "all grown up". I'll just have to wait for the teacher to give me the answer.

There is the same amount of alcohol in the water bucket as there is water in the alcohol bucket. The percentages as the same.
If you have trouble seeing this, it might help to increase the amount exchanged - say, instead of a cup, make it one-half of the water into the alcohol, etc.
Try it - it's not that hard to figure out.

lol Bo. I guess I'm just too lazy to expand my mathematical mind! I'm one those who sees. x/2 times x/4 = ? and says who cares?? I send all mathematical problems from my kids to my lovely wife. She handles that! I handle the reports and such!

I'd hafta agree with Tims logic
Brian

But if both buckets were full, the first ya dump into will just run over, than ya take a cup out it will be one cup from full. The other one will be filled back up completely with the cup you ad to it.

hm, now I'm really confused. and have a wet ring on the carpet to clean up.

Brian

Ah, the ole diversion game. You're trying to get off without answering the question?
Worked with your teachers, did it?

I have to agree with Kevin Jones. I just think about it for ooooh 3-4 seconds and then say who cares. I have to go take a nap now after all that thinking I am tired.

Kevin Pearson

This is a puzzle. It is designed to make one think, control the mind, imagine. Just to work it out is a pleasure - one of the real joys of life.

lol. No offense, Bo, but I find it faaarrr from a pleasure! But go ahead, enjoy torturing yourself .

Have you ever lifted a weight to strengthen yourself? To challenge the mind is to exercise it, to find new ways of thinking, to get rid of the fat and sloppiness.
As one who challenged the standard way of thinking, you need to look no further than our host, Ricky G. He solved a problem (how to clean carpet), and had the joy of saying - "Aha, I've got it."
Did that involve some heavy thinking? Was it fun?
Yeah.

Bo,
I don't mind a little heavy thinking at all......just not in things I perceive as math!! lol
You wanna talk about the origins of the universe or why I believe there is a God or some historical data, I'm all ears!
Talking about measurements, for me personally, just don't tickle my whistle!
I think it's great for people who like...my wife loves stuff like that. I'm just having fun with ya!

O.K. - let's try an easier one. The arithmetic is at most 4th grade. If you have to, get your wife to help you.
Say you have a trip of 80 miles. You want to average 40mph for the trip, but you find to your disgust that you only average 20mph for the first half of the trip. You're determined to averaqe 40mph for the trip.
So,how fast do you have to go the 2nd half to average 40mph?
If you don't get this one......

I turn around and go back!

Wouldn't that be called averaging zero mph?