Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.PCS 1/10/84; site ahutb.UUCP Path: utzoo!watmath!clyde!cbosgd!ihnp4!houxm!ahuta!ahutb!leeper From: leeper@ahutb.UUCP (m.r.leeper) Newsgroups: net.jokes,net.puzzle Subject: Re: Re: Re: Short-swords Message-ID: <535@ahutb.UUCP> Date: Thu, 7-Mar-85 22:55:13 EST Article-I.D.: ahutb.535 Posted: Thu Mar 7 22:55:13 1985 Date-Received: Sat, 9-Mar-85 07:13:14 EST References: <233@tekred.UUCP> <222@wuphys.UUCP> <101@ucbcad.UUCP>, <324@talcott.UUCP> Organization: AT&T Information Systems Labs, Holmdel NJ Lines: 57 Xref: watmath net.jokes:11246 net.puzzle:578 REFERENCES: <233@tekred.UUCP> <222@wuphys.UUCP> <101@ucbcad.UUCP>, <324@talcott.UUCP> Using finite differences and extrapolating up from lower dimensional cases, the answer is easy to see, but probably harder to prove. Dividing up a line with n points you get n+1 pieces. The first set of difference are all ones and all after that are zeros. 1 1 2 0 1 0 3 0 0 1 0 4 0 1 5 Dividing up a plane with lines you get the first set of differences are the values from the previous case: 1 1 2 1 2 0 4 1 0 3 0 0 7 1 0 4 0 11 1 5 16 One can see this is correct because the second cut can intersect the first cut, making four pieces. The next cut can intersect two previous cuts, adding three pieces. The next cut can interect all three previous cuts adding four more pieces, etc. 1 1 2 1 2 1 4 2 0 4 1 0 8 3 0 0 7 1 0 15 4 0 11 1 26 5 16 42 The n-th term is (n^3 + 5*n + 6)/6 Twenty cuts will give you 1351 pieces. Mark Leeper ...ihnp4!ahutb!leeper