NeoPets Riddles (Lenny Conundrums) and Answers Here

markr wrote:

Roly_Poly:
I also assumed that evaporation occurs in the first minute.

After 334 minutes, I have the volume of water at 4.67648+ cubic meters.
After 335 minutes, I have the volume of water at 4.68005+ cubic meters.

The bath holds 4.67653+ cubic meters.

ok you are right. I forgot to add in the evaporation in the last minute. duhhhhh.... this darn adult ADD.......

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007penguin wrote:

we have to round to the nearest minute....

No, you have to round up to the nearest minute. There's a difference.

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I worked out the spreadsheet independently of you guys (before tapping into any of the answers I've seen in this thread) and got result exactly the same as that of markr.

So the answer gotta be 335 minutes. because at 334 minutes we are just a liiiiitle bit off, and we are specifically asked to round *UP* to nearest minute - not to just round to nearest minute.

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I't probably 334, then.

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I meant 335.
Sorry.

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Ok, now I'm getting the answer at 158 minutes.

My formulas in Excel seem flawless to me, but I'm fairly likely to be wrong. I've got the 4/3*pi*r^3 (well, I combined 4/3*3.14159 because I couldn't find the pi button and used that constant in all my equations, and I don't think that would affect it much since everything is to 6 decimals) then I use "(Sph1I-Sph1F)+(Sph2I-Sph2F)+(Sph3I-Sph3F)" to get the volume melted in one minute, then I divide by 5.845725 (2.5981*1.5) and subtract 0.0001 from that to get the height of the water in the tub. Is this wrong?

(Sph1I is Sphere 1 Initial Volume for that minute, Sph1F is Sphere 1 Final Volume for that minute, for reference.)

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I got about 329...but I did it by hand...I'm not sure how, though...

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Nique wrote:

Ok, now I'm getting the answer at 158 minutes.

My formulas in Excel seem flawless to me, but I'm fairly likely to be wrong. I've got the 4/3*pi*r^3 (well, I combined 4/3*3.14159 because I couldn't find the pi button and used that constant in all my equations, and I don't think that would affect it much since everything is to 6 decimals) then I use "(Sph1I-Sph1F)+(Sph2I-Sph2F)+(Sph3I-Sph3F)" to get the volume melted in one minute, then I divide by 5.845725 (2.5981*1.5) and subtract 0.0001 from that to get the height of the water in the tub. Is this wrong?

(Sph1I is Sphere 1 Initial Volume for that minute, Sph1F is Sphere 1 Final Volume for that minute, for reference.)

are you taking into concideration that the volume melted will change each minute?

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Roly_Poly wrote:

Nique wrote:
Ok, now I'm getting the answer at 158 minutes.

My formulas in Excel seem flawless to me, but I'm fairly likely to be wrong. I've got the 4/3*pi*r^3 (well, I combined 4/3*3.14159 because I couldn't find the pi button and used that constant in all my equations, and I don't think that would affect it much since everything is to 6 decimals) then I use "(Sph1I-Sph1F)+(Sph2I-Sph2F)+(Sph3I-Sph3F)" to get the volume melted in one minute, then I divide by 5.845725 (2.5981*1.5) and subtract 0.0001 from that to get the height of the water in the tub. Is this wrong?

(Sph1I is Sphere 1 Initial Volume for that minute, Sph1F is Sphere 1 Final Volume for that minute, for reference.)

are you taking into concideration that the volume melted will change each minute?

Yes, I also reduce the radius by 0.0015 every minute for all three spheres. I use that as the reference for the r value in the cells.

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rounding kills you in problems like these.... oh, okay, on edit, maybe 6 digits would be precise enough. I'm too lazy to check.

In Excel, you can use the pi() function to use the exact value ... well, a *more* exact value I mean. Wink

You can also use the Power function to avoid having to do the r*r*r stuff -- my volume formula looks like =(4/3)*PI()*POWER(r,3)

My final answer's not 335, though... I made each rowon my table correspond to the minute, starting at zero minutes. We have known radii and volumes of the three spheres at t=0. At t=1, radii are 1.5 mm less, and again we have known volumes. In addition we have the change in volume -- the difference between the new volume & the volume of the sphere in the row above. Add the three volume changes, subtract the volume of (area of tub x 0.0001m), and add the previous row's grand total. Pick the second row and drag down a few hundred rows. I reached the final tub volume before the smallest snowball melted -- if I hadn't, I would have had to make sure that column wasn't contributing to the totals anymore...

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phaseolus wrote:

rounding kills you in problems like these.

In Excel, you can use the pi() function to use the exact value ... well, a *more* exact value I mean. You can also use the Power function to avoid having to do the r*r*r stuff -- my volume formula looks like =(4/3)*PI()*POWER(r,3)

My final answer's not 335, though...

Rounding can kill you, but not when you want 0 decimal places and you're counting 6 of them in your calculations, then taking the result of that 6-decimal at the bottom of the spreadsheet. Excel accepts r^3 just as easily as POWER(r,3) or r*r*r, so I don't think that's my problem, either.

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i started by converting everything into mm that way i don't have to worry about it later when everything is cubed

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Roly_Poly wrote:

i started by converting everything into mm that way i don't have to worry about it later when everything is cubed

I find it easier to work with whole metres so that I don't forget to divide by 1000 later on, myself. =)

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How are you people doing this with Excel?!?

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Nique wrote:

Rounding can kill you, but not when you want 0 decimal places and you're counting 6 of them in your calculations, then taking the result of that 6-decimal at the bottom of the spreadsheet.

Rounding will kill you in this problem. You only need 0 decimal places for the number of minutes, but you better be more accurate than that when computing volume.

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ok i think im done for this week. I prematurly entered my answer and got it wrong(Dumb me). But my final answer is 335 minutes. talk to you all next Thur.

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markr wrote:

Nique wrote:

Rounding can kill you, but not when you want 0 decimal places and you're counting 6 of them in your calculations, then taking the result of that 6-decimal at the bottom of the spreadsheet.

Rounding will kill you in this problem. You only need 0 decimal places for the for the number of minutes, but you better be more accurate than that when computing volume.

Forget it, I put in my answer as 334, I've already won the avatar from the conundrum back with "underwater fishing", I'm just doing it for something to do while I'm on summer break every Thursday.

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But Nique, the evaporation takes place through out the minute so by the end of the minute it will still be 49735.73073 mL short of being full

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Roly_Poly wrote:

But Nique, the evaporation takes place through out the minute so by the end of the minute it will still be 49735.73073 mL short of being full

I factored in the evaporation in every line in the formula in the cell. I did that in the first cell way at the top for minute 1 and that's what I copied down to the rest. Now I'm leaving for the night because today is not a good day and I don't feel like blowing up at complete strangers over something that's not their fault, it's mine for being an idiot and moody. Sorry if I'm being or if I have been rude, it's just been a loooong day.

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TheLatterRain wrote:

How are you people doing this with Excel?!?

Here's my solution. Cut this, paste it into Notepad, and save it with a .csv extension. Then open it with Excel. You should end up with 8 lines in Notepad: 4 lines with text and formulas, a blank line, then 1 short line and 2 long lines. Depending on how the cut/paste works, you may have to rejoin the 2 sections of the 2 long lines. [edit: I tried it, and it doesn't require rejoining]

Plug your number of minutes into A7 or A8. You want the smallest number in column J that is greater than or equal to the number in H3.

,sphere 1,sphere 2,sphere 3,total,,,bath,,
radius,0.45,0.75,0.9,,,area,=6*0.75*0.75*SQRT(3),,
volume,=B2^3*PI()*4/3,=C2^3*PI()*4/3,=D2^3*PI()*4/3,=SUM(B3:D3),,volume,=0.8*H2,,
melt rate,0.0015,0.0015,0.0015,,,evap rate,=0.0001*H2,,

minute,r1,r2,r3,v1,v2,v3,melted,evaporated,net result
334,"=MAX(0,B$2-B$4*$A7)","=MAX(0,C$2-C$4*$A7)","=MAX(0,D$2-D$4*$A7)",=PI()*(4/3)*B7^3,=PI()*(4/3)*C7^3,=PI()*(4/3)*D7^3,=$E$3-SUM(E7:G7),=-A7*$H$4,=SUM(H7:I7)
335,"=MAX(0,B$2-B$4*$A8)","=MAX(0,C$2-C$4*$A8)","=MAX(0,D$2-D$4*$A8)",=PI()*(4/3)*B8^3,=PI()*(4/3)*C8^3,=PI()*(4/3)*D8^3,=$E$3-SUM(E8:G8),=-A8*$H$4,=SUM(H8:I8)

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NeoPets Riddles (Lenny Conundrums) and Answers Here

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