Lenny Conundrum #125

[mrlrules]

Congratulations! You have guessed correctly in the Lenny Conundrum game (Round 124). We have given you 1666 NP!

I put "forever". It's an OK payout, better than the usual 300 NP.

[o_0]

One of the easiest "hard" ones comes up, and I'm in New York.

I wanted that Snowbunny.

[bex]

Congratulations! You have guessed correctly in the Lenny Conundrum game (Round 124). We have given you a Snowbunny Bath Puff, an Avatar, and 1666 NP!

I am so excited. I wasn't sure if I was right or not, but I figured I should go ahead and put that it would never happen so maybe I could get the avatar! I was about ready to give up on ever getting that avatar as well.

[AySz88]

"Not enough ice" is what I wrote - guess they were pretty liberal on matches! I thought for sure that there'd be some sort of obscure detail that'd make it possible for the ice to fill the tub....

[kulana]

The new lc is up...and it's continued.

Princess Amira was furious. "All I ask is to have a bath full of freshly sun-melted glacial ice, and my servants can't even get that right!" She ordered them to empty out her bath and start over with new glacial ice.


This time, they returned with three ice spheres: one was 0.9 meters in diameter; one was 1.5 meters in diameter; and the last was 1.8 meters in diameter. They all started melting at the same time. Also, the water in the bath evaporated at a rate of 0.1mm of depth per minute.

Otherwise assuming the same conditions as last week's Lenny Conundrum, how many minutes will elapse before the bath is completely full? Please round up to the nearest minute.

[XenaAndGabrielle]

I'm working on it. The spread sheet is giving me problems.

Edit: Well, I have an answer ... unsure if I am correct, though. It is 4 digits long.

Edit Edit: I've back calculated ... and my 4 digit answer does indeed make sense. Assuming I didn't make a stupid mistake.

[AySz88]

I got a three-digit answer by solving a cubic by calculator.... *worried* Is anyone else getting that the water level actually drops in the middle?
*edit* Oh shoot. I know what I did. >.< Got the 4-digit number, but I already submitted.

[mrlrules]

I got 3 digits. When they say the ice melts 1.5mm per minute, that means the radius goes down by 1.5mm, right? Because if the diameter is 1800mm, then it will go down by 1.5mm on both sides, to 1797mm, making the radius go from 900mm to 898.5mm. Am I right?

EDIT: Realized my mistake. Forgot to cube the radius. I'm working on my other answer now.

[digitel_anime_fan_20]

Can someone explain to me the previose coundundrums answere? Why would it never fill?

[Medusa]

Can someone explain to me the previose coundundrums answere? Why would it never fill?

I would assume that: the volume of the original sphere with a diameter of 2 meters was less than the volume of the hexagonal bath measuring 1.5 meters on a side, and 0.8 meters deep. Hence, even if all the ice melted it would not be enough to fill the bath.

[weirdguy]

I never really expected to put that down. I hate how that always happens.

In any case, my spreadsheet wasn't wasted. But all those rates at the same time took some setting up. I got 3 digits.

[XenaAndGabrielle]

I never really expected to put that down. I hate how that always happens.

In any case, my spreadsheet wasn't wasted. But all those rates at the same time took some setting up. I got 3 digits.

Grr. It seems I calculated wrong. I hate that. I read that the water evaporated into the bath at a rate of 0.1mm / minute.

Sigh ... I hate realizing I screwed up.

Last edited by XenaAndGabrielle on Fri Jul 15, 2005 8:47 am, edited 1 time in total.

[Medusa]

Edit: Everyone make sure you carefully consider when you are doing your calculations where the evaporation rate is from And the water evaporating will be disappearing into thin air!

[mrlrules]

Well, I finally got my other answer, and I still have 3 numbers.

Also, digital_anime_fan, the reason it never fills is that the volume of the sphere is 4.189 m^3 (4/3*pi*r^3) and the volume of the hexagonal bath is 4.678 m^3.

[digitel_anime_fan_20]

Also, digital_anime_fan, the reason it never fills is that the volume of the sphere is 4.189 m^3 (4/3*pi*r^3) and the volume of the hexagonal bath is 4.678 m^3.

Ah, thanks.