Which bowl does he choose to pour their taster from?

Which bowl does he choose to pour their taster from?

Ankita Katdare

Administrator

Updated: Oct 26, 2024

Views: 1.1K

Okay, so a host of a party has a pint bowl of water (A) and a pint bowl of fruit cocktail (b).
First he pours half a pint from the water bowl (A) into the fruit cocktail bowl (b) and then mixes it thoroughly. Now he pours half a pint of the fruit cocktail/water mix (b) into the water bowl (A) and mixes that thoroughly.
He repeats the pouring from (A) to (b) and then from (b) to (A), mixing thoroughly each time, only this time only a quarter of a pint of the mixed fluid is poured each way.

Now the host asks his first guest if they want to sample a "strong fruit cocktail" or a "weak fruit cocktail"?
The guest says they would like a sample of the "strong" fruit cocktail.
Which bowl does he choose to pour their taster from?

0

Replies

Howdy guest!

Dear guest, you must be logged-in to participate on CrazyEngineers. We would love to have you as a member of our community. Consider creating an account or login.

Replies

akash.kasina

Member • Jun 1, 2012

the bowl which we filled with with fruit cocktail contains the highest concentration among both bowls!😀

Are you sure? This action cannot be undone.
Cancel
KenJackson

Member • Jun 6, 2012

I'm missing something here.

"A pint bowl of water" sounds like a container that has a capacity of one pint and is full. If you start with two bowls that are full of their respective fluids and pour one into the other, the other will overflow. Is that part of the puzzle, or do I just misunderstand?

Are you sure? This action cannot be undone.
Cancel
Vassilya

Member • Jun 10, 2012

Assuming they didn't overflow (see previous) then they would be equal after the first exchange, methinks

Are you sure? This action cannot be undone.
Cancel
silverscorpion

Member • Jun 10, 2012

After the first swapping, the concentrations of water and the cocktail in both glasses will be equal, I think.. Similarly after the 2nd time too..

Are you sure? This action cannot be undone.
Cancel
Sagar07

Member • Jun 11, 2012

Bowl b...

Are you sure? This action cannot be undone.
Cancel
ashie

Member • Jun 13, 2012

Bowl A

Are you sure? This action cannot be undone.
Cancel
KenJackson

Member • Jun 13, 2012
Since I didn't get an answer to my question, I'm going to make some assumptions:
1. The phrase "a pint bowl of" means a container that holds exactly one pint and is exactly full,
2. "Fruit cocktail" is a liquid with similar properties to water (no chunks),
3. When something is poured into a full bowl, it's quickly poured into the center of the bowl such that only the existing fluid overflows, none of the fluid being poured in overflows, and
4. It's somehow possible to thoroughly mix a full bowl without spilling any.
Let's start:

1) Pour half a pint from water (A) into cocktail (b) and mix.
Overflow: 1/2 pint of cocktail, leaving:
(A) 1/2 pint of water
(b) 1 pint of 50% water

2) Pour 1 pint from (b) to (A) and mix.
Overflow: 1/2 pint of water, leaving:
(A) 1 pint of 50% water
(b) empty

3) Pour 1/4 pint from (A) to (b) and mix.
(A) 3/4 pint of 50% water
(b) 1/4 pint of 50% water

4) Pour 1/4 pint from (b) to (A) and mix.
(A) 1 pint of 50% water
(b) empty

Answer: Bowl (A) has the "strong" fruit cocktail, 50%, because bowl (b) is empty.
Are you sure? This action cannot be undone.
Cancel
Sagar07

Member • Jun 14, 2012

Well, let me justify my ans...
Suppose both bowls contain 64 liters each..

Now, 32 liters of water is poured into bowl b...

So, bowl b=32 liters of water+ 64 liters of cocktail= 96 liters in the ratio of 1:2 of water and cocktail...

Now, 48 liters(16 liters of water and 32 liters of cocktail) of bowl b is poured into bowl A...

So, bowl A=32 liters of water+ 32 liters of cocktail + 16 liters of water= 80 liters in the ratio of 3:2 of water and cocktail...

Now, 20 liters(12 liters of water and 8 liters of cocktail) of bowl A is poured into bowl b...

So, bowl b=16 liters of water+32 liters of cocktail+ 12 liters of water + 8 liters of cocktail= 68 liters in the ratio of 7:10 of water and cocktail...

Now, 17 liters(7 liters of water and 10 liters of cocktail) of bowl b is poured into bowl A...

So, bowl A=36 liters of water+24 liters of cocktail+ 7 liters of water + 10 liters of cocktail= 77 liters in the ratio of 43:34 of water and cocktail...

Ratio of water and cocktail
Bowl A= 43:34
Bowl b=7:10

So, Bowl b contains stronger fruit cocktail...

Note: Assuming bowls didn't overflow...

Are you sure? This action cannot be undone.
Cancel
Ramani Aswath

Member • Jun 14, 2012

Given that the volumes of both bowls are equal after the double exchange, the concentration of of fruit cocktail in the water bowl and the concentration of water in the fruit bowl will be the same. This is true for every exchange. Curiously this is true even if there was no mixing at all.
In my opinion both will reach equal dilution asymptotically. In real terms the original cocktail bowl will always have the higher concentration of the cocktail

Are you sure? This action cannot be undone.
Cancel
KenJackson

Member • Jun 14, 2012

Sagar07
Suppose both bowls contain 64 liters each..
That contradicts the problem statement. Each container was described as "a pint bowl."
A <a href="https://en.wikipedia.org/wiki/Pint" target="_blank" rel="nofollow noopener noreferrer">Pint</a> is two cups or 16 floz (about 474 mL).

Are you sure? This action cannot be undone.
Cancel
Sagar07

Member • Jun 14, 2012

KenJackson
That contradicts the problem statement. Each container was described as "a pint bowl."
A <a href="https://en.wikipedia.org/wiki/Pint" target="_blank" rel="nofollow noopener noreferrer">Pint</a> is two cups or 16 floz (about 474 mL).
Well, then consider mL instead of Liters......

Are you sure? This action cannot be undone.
Cancel