3 ms·
> Do I understand correctly that you can shuffle the image's rows (or columns) without losing that effect? Yes, but a dramatic reduction in complexity still le
by philh 15y ago
> Do I understand correctly that you can shuffle the image's rows (or columns) without losing that effect?
Yes, but a dramatic reduction in complexity still leaves a lot of complexity.
Your conditions seem to be a lot simpler than they originally appear. If I interpret you correctly, we're drawing seventeen 4-tuples of seventeen-bit numbers such that
> every tuple is a subset of one of the sets in the second set
"the elements of each tuple have no bits in common", and
> every drawn number is contained in one of sets in the first set
"each number has at most one bit set".
But there are only eighteen seventeen-bit numbers with at most one bit set, or seventeen if you exclude 0 (which seems reasonable). So isomorphically, we're trying to find seventeen 4-tuples of distinct numbers less than seventeen.
This is indeed easy (there are (17 choose 4) = 2380 of them), but I don't understand what you hope to do with these. At any rate, I don't think they particularly help solve the problem at hand.
- guard-of-terra 15y agoNope, the second condition would be "each i-number is from a set where no two numbers share more than one common bit" You can pre-compute that set of sets (of course throwing away numbers with just 0, 1 or 2 bits set because we suspect they would slow us down without delivering) fit them in memory and then crunch the problem like a bug. I've thrown together two simple scripts (in perl) which show that the known solution fits both of my rules. Hopefully I can write a program that would find solutions for any given NxM (or tell that no solution exists) tomorrow or something like that. Still I suspect the solution would hit the wall because e.g. sets would be too big therefore the program would take actual ages to run, but one can surely hope?
- philh 15y agoOh, I read AND but was doing OR. My mistake. > Still I suspect the solution would hit the wall because e.g. sets would be too big therefore the program would take actual ages to run, but one can surely hope? I suspect something will go wrong, and this seems to me the obvious place for it to fail. But I expect it to fail mostly based on "if it was that easy, someone would probably have noticed", not because I have any particular insight into the problem.
- guard-of-terra 15y agoI have a same gut feeling, but one of my professors told us how the discoveries are being made: Everybody know that some thing is impossible to do. But one person who didn't know that accidentally does it. Right now I have one type-1 set having 36 numbers in it. The first numbers are 7, 25 and 42. I like it.
- guard-of-terra 15y agoAnd the first rule would be "the elements have no bits in common, but together (ORed) they have all 17 bits" That's almost XOR(i in S) = -1 but not really