Ponder This

March 7, 2005 4:42 AM

Ponder This.'You are cordially invited to match wits with some of the best minds in IBM Research.' Monthly puzzles, with solutions, going back to 1998.
posted by plep (12 comments total)

This is good, but a bit beyond my analytical and math skills sometimes. I think I found it from a very early AskMe, but I can't recall, exactly.
posted by Plutor at 5:02 AM on March 7, 2005

ok.. that's a challenge.. i'm on the 011001 cube puzzle.. :D
let's see if i can whip a loop that checks all possibilities..
posted by zenzizi at 5:13 AM on March 7, 2005

Super... I read the March puzzle over and I am feeling about as bright as a fern at this point.

*plays with office toys*
posted by fluffycreature at 6:10 AM on March 7, 2005

Oy, all possibilities? 6^3 bits is 2^(6^3) possible values. That's, er, roughly 1.053*10^65. Good luck.
posted by Plutor at 6:15 AM on March 7, 2005

Are you pondering what I'm pondering, Pinky?
posted by BlueMetal at 7:13 AM on March 7, 2005

It could be a trap: Mercury Rising.
posted by veedubya at 7:41 AM on March 7, 2005

To put Plutor's observation in perspective:

Even if your computer could check the validity of
a potential cube in 1 nanosecond, to check all potential
cubes would take much longer then the current age
of the universe.

In fact, I think the number of years it would take
is closer to the number of atoms in the Earth.
posted by toftflin at 7:51 AM on March 7, 2005

So, there has to be a quicker way, then.
posted by carter at 7:57 AM on March 7, 2005

Yay! There goes my week.

(/me loves stuff like this)
posted by devbrain at 8:00 AM on March 7, 2005

yea i got most of it modelized..
and now i realize the high numbers involved..
trying to find shortcuts to eliminate the most checks..
posted by zenzizi at 8:22 AM on March 7, 2005

ok so i gave up being able to check all possibilities..
now i just loop and check random combinations lol..
maybe i'm gonna make a hit in the day..
i see someone was just added as a 1st solver tho..
posted by zenzizi at 8:59 AM on March 7, 2005

Here's the way I'd solve this months puzzle (and perhaps will when/if I have more time): Basically, solve it Rubik's cube style

1) whip up a program that allows me to input a starting config (e.g. the one they use as an example)
2) the program would tell me how many unique signatures I have in each of the three directions (e.g. X:26, y:30, x:32)
3) Then I can do a few basic operations
a) tweak a bit (optimal at intersecting dup. signatures)
b) "flip" a signature (this would not change the unique sig count in one direction but may lower it in the others)

And so on, just play with it, using your own brain and see if you can get all three counts to equal 36. Also, its obvious there is more than one solution.
posted by vacapinta at 1:44 PM on March 7, 2005