Lenny Conundrum #134

[XenaAndGabrielle]

Congratulations! You have guessed correctly in the Lenny Conundrum game (round 133). You have won 2151 NP!

Because you were in the first 250 to guess correctly, you also have been awarded a Sand Blade, and receive a trophy and the Lenny Conundrum avatar!

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I got 2 neomails ... the first with only the NP message ... and then a second one that I quoted above with the item.

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AND ... WOO HOO! *DRUMROLL PLEASE* ... ... ... ... ... ...

I *finally* got a gold trophy for the LC! I knew I had gotten in early this time ... so I hoped that it would be in time (and correct!) WOO HOO! I'm so happy! Yay me!

The answer was: 22.38

My excel notebook is at home. Someone else (Neomania, I think) had an actual solution that can be posted.

In words ... you have to be careful about covering the sides and the tops of the blocks (that were uncovered). When you got to a place where you only had to cover the sides of a block ... just find the fraction that needed to be covered to obtain that amounts of surface area.

So I managed to upgrade my LC trophy. I was beginning to think it wasn't actually possible.

[neomania]

THIS IS THE SOLUTION FOR LC 133!I will take this time to give and explicit formula for finding the answer. Ok i start out by defining some notation. n (or i) is the number of the row of the pyramid. with the top n=1 and bottom n=100. sum(1,k)[i]= 1+2+...+(k-1)+(k)=(k^2+k)/2. sum(1,k)[1]=k. Allright because of gravity the pryramid is being buried from bottom up. The surface area for a row = (.63*.97*4)(i) + (.97^2)(2i-1).

Remember we are working from top to bottom so we need to find a formula for the sum(n,100)[i]. This is sum(n,100)[i]sum(1,100)[i]-sum(1,n)[i]+n= 5050+n-((n^2+n)/2). Ok we need to find the row that the sand pile reaches to. so we have to solve the quadratic (i wish i had equation editor) . The pyramid surface area (bottom up is then:
sum(n,100)[ (.63*.97*4)[i]+(.97^2)(2[i]-1)]=12616.8676 [ m^2]

(.63*.97*4)(i)(5050+n-((n^2+n)/2)) + (.97^2)(2(5050+n-((n^2+n)/2))-(100-n+1))=12616.8676. we solve the quadratic and get n=65.7... But since these formulas are for sum of integers we round up this answer (Remember we are working from bottom of pyramid to top) to 66. We plug 66 back into the formula and get an answer for the surface area. this answer is less than 58 percent of the entire surface area of the pyramid. This difference comes from the 65th row

But we only need area from the side part (vertical) of this row. We take our deficit in area DA and find the depth d of the pile from the 66 row to the partial 65th row. DA= (d*.97*4*65). Then the height of the pile is just H = (35*.63+d), where the 35 is from the number of rows from the 100 to 66 row. and we are done.

Last edited by neomania on Fri Sep 16, 2005 1:24 am, edited 2 times in total.

[Cranberry]

I got two neomails, too -- one with just the NP notification, and one with the trophy/prize notification. I got upgraded to silver!

[sirclucky]

me too cranberry(got silver and the prize)

I was lazy a burte forced it via excel. Shouldve solved it quicker, but not fast enough for gold me thinks, so it doesnt matter. *huggles silver trophey*

[stampsyne]

I got GOLD. Oddly, I had silver from last LC; now my trophy says X2 in Gold.

[XenaAndGabrielle]

I got GOLD. Oddly, I had silver from last LC; now my trophy says X2 in Gold.

Yeah, I had silver from an LC a long time ago ... this week's gold gave me the "2x" thing as well.

Same with Better than you. I only had bronze in that one from a long time ago ... but got the gold this week and now it say 2x.

LC gold and BTY gold in the same week (day!). How cool how cool!

New one is up:
Suppose you have, say, a stone tablet of some sort. The tablet has 16 pieces missing. But lucky you, you have the pieces! You can tell by looking at the pieces which ones are the four corners, which ones are the eight side pieces, and which ones are the inside pieces. Otherwise, you can't tell where on the tablet they should go or how they should be oriented.

If it takes 90 seconds to place all of the pieces, how many days will it take to try every possible combination? Please round to the nearest full day.

Last edited by XenaAndGabrielle on Fri Sep 16, 2005 12:42 am, edited 1 time in total.

[thestarthatislucky]

Suppose you have, say, a stone tablet of some sort. The tablet has 16 pieces missing. But lucky you, you have the pieces! You can tell by looking at the pieces which ones are the four corners, which ones are the eight side pieces, and which ones are the inside pieces. Otherwise, you can't tell where on the tablet they should go or how they should be oriented.

If it takes 90 seconds to place all of the pieces, how many days will it take to try every possible combination? Please round to the nearest full day.

[XenaAndGabrielle]

I'm a little confused about "how they should be oriented"

Do you think they just mean "where on the tablet they are?"

Or

Do you think they mean "how the individual piece gets put down on the tablet"

I.E. if they were squares, there are 4 different orientations that it can be put on the tablet.

The question seems to be trying to make a distinction between these 2 things ... since it says "you can't tell where on the tablet they should go or how they should be oriented."

I ask, because I am getting an answer I don't need to round.

[datrulegend]

Hint: It probably involves factorials. (I said probably 'cause even I'm not 100% sure ). I'm in Algebra 2 with Trig, but I still LOATHE probabilty. It's !!!

I'm getting a whole number answer also...in response to Xena.

[matchbow]

ORIENTED?! dude, i totally didn't even consider that at all. i just put my answer as fast as i could. from what i can see from the pic, there doesn't seem to be any pieces that can be oriented more than one way. and they better mean that every piece will be tried in every spot regardless of shape. no wait, that would mean that they'd try different orientations. crud

[XenaAndGabrielle]

ORIENTED?! dude, i totally didn't even consider that at all. i just put my answer as fast as i could. from what i can see from the pic, there doesn't seem to be any pieces that can be oriented more than one way. and they better mean that every piece will be tried in every spot regardless of shape. no wait, that would mean that they'd try different orientations. crud

It just seemed weird wording.

"You can't tell where on the tablet they should go or how they should be oriented."

Hopefully they were just saying the same thing "over again"

I do get an answer that doesn't need to be rounded, though. Hopefully it is what they want.

[datrulegend]

ORIENTED?! dude, i totally didn't even consider that at all. i just put my answer as fast as i could. from what i can see from the pic, there doesn't seem to be any pieces that can be oriented more than one way. and they better mean that every piece will be tried in every spot regardless of shape. no wait, that would mean that they'd try different orientations. crud

Lol. Poor you One thing I've learned over many fruitless tries and one bronze trophy is that you have to agonize over the question. Think about it from many different points of view. And always ask for help from somebody better at math than you. I asked my dad and got a completely different answer...that seems more right. Still a whole number tho. As in no rounding required. Well, good luck to all. My work with this conundrum is done!

[XenaAndGabrielle]

Since they didn't give us what the shape of the tiles were ... I think we have to assume that they just meant "try each piece in the places that we know it fits"

Otherwise, the answer would be different depending on what the shape of the tiles were.

[md0b]

can i confirm with anyone plz?

[Jez]

Can I confirm my answer with anyone, please?