Re: Pattern Possibilities

On Aug 15, 2:05 pm, "[Mr.] Lynn Kurtz" <ku...@xxxxxxxxxxxxxxx> wrote:
On Wed, 15 Aug 2007 11:16:32 -0700, inke...@xxxxxxxxx wrote:
Ink an 8" x 8" grid on 95 pieces of paper. Check one square out of
the 64 squares of the grid with pencil, or leave the grid blank. Do
this for all 95 pieces of paper.
Erase all checks. Repeat.

How many different patterns of check placement can you create before
repeating yourself?

By "repeating yourself" do you mean each of the 95 sheets in some
order have the same marks as some previous version of the 95 sheets in
the same order? Holding the sheets right side up? If so...

On page 1, there are two choices (check or no check) for each of the
64 squares for 2^64 distinct patterns. Ditto for page 2 thru 95. So
you get (2^64)^95 =

1829673664174779885002165504637402565007523331001975600418845818612812
8244356029898808963344994683698369631499211643708674655292741681502209
1324873677513387043923211145477917136833698474998392989741636792486000
9281763410001179573048915011290676059616616707330605798907756600122916
5861411380406909010591986037182080878016674457118851216662328109859327
0817181614297552879649808345925121706295739480817656585628368821120497
6653945606242886647248765778276815274539231529154285783898100586922674
9624673505776012095188911523119323454844958382587057846905771767705037
3356057205180717001569743940752269113669157378653258136302544838219625
8830777154827433308531340880252208387873357593750577369925342225778979
0968995168034639215704336089980566586952548841173235552059778455345723
8945335087309626177555457993300628456963926476535335113326425043829999
0760559034725552708648425788336654244916319466739826380916694556539432
7128793970565698722048728108474793853627055720080113845979219660186486
3384086929465373594944610678265255091810017899879217317523380742467705
2291010904753009138799474166309238859180856040822679584096982525658561
4314893713418293552477275050464598559624541926524171086336662385003922
9301388392332631174896856495222977034143259867468296403631707925065640
4519237746490178204547561770898594697708210107913716416745069626268008
1311138578251192498259328564947196745547074866381290462350466893657634
5411499519342005414601180711821799780036810961227501683227277350258142
8284320373135500693584090400992175642549852247083517426434831602949288
3824482741306901018545227105688563740678230658042978948967489825836763
2513255497335353144595086491979046765421882764040668377554850216049991
0480039337400398228744707560343257718564799770729645607999459255833013
6712574831416726787521462534170628122850561828692507729353267420735404

You're off by 11 orders of magnitude.


ways. Of course, if you didn't mean that, you need to be more specific
in your question.

--Lynn


.