EventHorizon

Since zoris didn't answer the last part of question 1....

I had thought a while about trying to figure out how adding more towers would affect the number of steps needed. It turned out to be an interesting answer (I love it when answers involve Pascal's triangle (represented in the answer by nCr))....though I don't know why it is as it is......yet. I wrote some c++ code that given the number of towers and disks it would do breadth first search to find the least number of moves to move all the disks from one tower to another. It reports the number of steps and gives the sequence of states/moves. I altered it later to just go halfway (till the biggest disk is moved) since the rest is fairly obvious. I included some code.....just no comments on how bad/cryptic/not fault tolerant/not robust it is I included some text files that shows the output I looked at to come up with my solution. I basically ran the code till it would crash because of integer overflow/out of memory and included the results. I may rewrite it by taking a different approach to allow larger numbers for the amount of towers and disks....later. In the text files the state is listed as position of the disks going from smallest to biggest... so it starts at 0 0 0 0 0 for 5 disks....which mean all disks are on tower 0. The second state may be 1 0 0 0 0....which means all the disks but the smallest are on tower 0, and the smallest is on tower 1.

Lets see how rusty my Bayesian reasoning is....

you could use the quartic formula (not recommended), or just plot it on a calculator and then use synthetic division to remove roots that you find. According to brhan's post (first on page 3) your equation is right.

Expand (x-2)(y-2)(z-2) (the unshaded cubes) and subtract it from x*y*z (total). Thats the way I started the 2d one.

Certainly. I'm fairly new to this site too, but like to explain things to people. There are no dumb questions so long as you learn from them.

Lets say the rectangle is 1Xx. Then there are x total squares, and all of which are shaded (all on the border). There are no unshaded squares. Therefore the number of shaded squares are not equal to the number of unshaded squares. So rectangles of this sort will not work.

He would need to go 50 + x backwards to reach his original position. 50-x would be the distance the soldier would need to go _forward_ after delivering the letter to be where the leading soldier will be once the platoon moved 50m.

To get to where he will need to eventually be, he would need to move 50m. From there, he needs to move x more to reach the leader. He then needs to move x back....not 50-x.... to get back into position.

That would be true if the platoon wasn't moving. The platoon moves forward 50m during this whole process.

Too bad my edit time expired...so here's a new post. Any degenerate case of a rectangle (either dimension is 0) will work. So....how about in 3 dimensions....where each border cube is "shaded"?

edited to remove any confusion with bases

yes, but I was simply finding the values could be substituted for the width and length to fulfill the "number of shaded squares equals the number of squares in the center." 0X0 can be argued not to be a rectangle, but it is still a degenerate case of a rectangle. So I guess I should have said "degenerate case" instead of "trivial answer." I still believe it could/should be included.

They are right triangles. I guess I should have posted a picture too....I thought aatif's would be sufficient.

It's 273.15.

Ahh....I didn't think the dealer was another player.