[Guest]

At a cocktail party you are given a glass filled with your host's special secret cocktail. Unfortunately, it's horrible! In an attempt to avoid insulting your host, you suggest that the cocktail might be improved by the addition of a scoopful of peppermint ice cream. What size scoop of ice cream should you select in order to displace as much of the cocktail as possible? See the figure below for dimensions.

(picture at http://hilltop.bradley.edu/~delgado/potw/p12.html the source of the problem)

This was a very interesting one and it took me a little while to solve. Good luck

[Guest]

r=h/(1+1/cos(theta))

If I will not fall asleep I will calculate this

Edited April 16, 2010 by det

[Guest]

Good morning

My first guess was wrong; I created the function of the sphere inside the glass (I checked the cases when the centroid above and under the upper side of the triangle(this two can be described by the same function)- this gives the maximum - and when the full circle is inside the triangle)

However I will not calculate the maximum of this function without specified h and theta values...

to check my calculation here is the radius of the ice cream for these conditions:

h=10

theta=pi/4

-> r=8.09105

probably there is an easy way to find the optimum

btw r=h*cos(theta) is a good approximation

Edited April 17, 2010 by det

[Guest]

The exact size of the cup's edge diameter? as in the equator of the scoop would be exactly on the edge of the cup

[Guest]

Hey ,i think the answer is 4/3 Pie h(cube)cotcube(theta)/Sincube (theta).

At a cocktail party you are given a glass filled with your host's special secret cocktail. Unfortunately, it's horrible! In an attempt to avoid insulting your host, you suggest that the cocktail might be improved by the addition of a scoopful of peppermint ice cream. What size scoop of ice cream should you select in order to displace as much of the cocktail as possible? See the figure below for dimensions.

(picture at http://hilltop.bradl...o/potw/p12.html the source of the problem)

This was a very interesting one and it took me a little while to solve. Good luck

[Guest]

Hey ,i think the answer is 4/3 Pie h(cube)cotcube(theta)/Sincube (theta).

Good morning

My first guess was wrong; I created the function of the sphere inside the glass (I checked the cases when the centroid above and under the upper side of the triangle(this two can be described by the same function)- this gives the maximum - and when the full circle is inside the triangle)

However I will not calculate the maximum of this function without specified h and theta values...

to check my calculation here is the radius of the ice cream for these conditions:

h=10

theta=pi/4

-> r=8.09105

probably there is an easy way to find the optimum

btw r=h*cos(theta) is a good approximation

[Guest]

the diameter should be (1/0) cm. But you're dividing by zero, meaning that the universe will be destroyed resulting in a complete cocktail displacement.

[bonanova]

This classic problem was at in a discussion of a

How do the solutions compare?

[Guest]

This classic problem was at in a discussion of a

How do the solutions compare?

My apologies bonanova. I searched the forum for the problem, but missed yours. Thank you for calling this to my attention.

[bonanova]

My apologies bonanova. I searched the forum for the problem, but missed yours. Thank you for calling this to my attention.

Not a problem. Done it myself even. You can't always find the right search words.

Just wanted to bring the past discussions to the table, along with the great drawings from the previous poster.

It's a fun problem, and, have we found a consensus?