# jimmyljb

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1.2) Lines in the plane.
What is the maximum number L, of regions defined by n lines in the plane?
L0 = 1
Ln = Ln-1 + n (n>0)
=>>   Ln = n(n+1)/2 +1

Suppose that instead of straight lines we use bent lines, each containing one “zig!", such as "<"
Zn = L2n - 2n = 2n(2n+1)/2+1-2n = 2n^2-n+1 (n>=0)

1.3) THE JOSEPHUS PROBLEM
In our variation, we start with n people numbered 1 to n around a circle,and we eliminate every second remaining person until only one survives.
J(1) = 1 ;
J(2n) = 2J(n) - 1 , for n > 1;
J(2n + 1) = 2J(n) + 1
==>>J(2^m+l) = 2*l+1;

for binary number
J(ABCDEF) = 2*BCDEFA + 1 (A,B,C,D,E,F = 0,1)
J(1...1...) = 1...1...   (A = 1)

posted @ 2006-07-19 01:33 jimmyljb 阅读(168) | 评论 (0)编辑 收藏

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