No meir, that's not true. #X# XXX
The 4 Xs are connected. 4 is divisible by 2, but you cannot tile the space with 2-ominoes. However, it's irrelevant to the question in the competition, because you cannot construct such a space by beginning with a rectangle and adding a single 2-omino. Paul Smith [email protected] On Wed, Apr 15, 2015 at 3:17 PM, meir <[email protected]> wrote: > The statement is correct. > When you aren't required to use a specific X-omino it is easy > to fill any connected shape divisible by X with X-ominos. > Only being required to use a specific X-omino causes problems but that is > not the case with the quoted statement. > > > On Wednesday, April 15, 2015 at 12:41:51 PM UTC+3, bigOnion wrote: > > The analysis says that whenever you are left with a connected blank > space (not necessarily rectangular) whose size is divisible by X - then you > can fill it up with X-ominoes: > > > > " If a connected blank area of size M is a multiple of X, it can be > guaranteed that there is a way to place M/X X-ominoes to fill in the blank > area. " > > > > It also repeats later. > > > > It seems that what is actually used in the proof is the claim in the > other direction: if you can force a blank space to be of size not divisible > by X then you win (no way to fill the blank space). > > > > The claim as stated doesn't seem quite right actually. Consider the case > of a connected blank space of size 4 whose shape is of one blank space with > three other blank spaces around it (adjacent to it). Then obviously there > is no way to fill this space with 2 2-ominoes. > > The claim in the analysis is not quite right. Maybe it can be right with > more restrictions and in a specific content, but not the way it is > currently claimed. > > -- > You received this message because you are subscribed to the Google Groups > "Google Code Jam" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/google-code/926eaf01-63b4-4280-881c-c390453ec6c2%40googlegroups.com > . > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "Google Code Jam" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/google-code/CAJej63LD3bgoYH%3D6QJRUeo6D6Sy8QzicyGSbRrdNbFmFsEfMjw%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
