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Spanning trees of a two-dimensional n-by-n grid graph

Views:429,Comments:0,Saved by 1 Sept. 8, 2008, 2:42 a.m. | spellscroll

Given a graph G constructed from a two-dimensional n-by-n grid, what is the number of spanning trees of G?

Tags: lattice(1) tree(1) graph(1)

birthday month

Views:352,Comments:0,Saved by 1 Sept. 8, 2008, 3:58 a.m. | spellscroll

Birthdays of 20 members of a club are assumed to be independently and
uniformly distributed over the twelve months. Let Z be the number of months
during which ...

Tags: probability(1)

open the lock by trying the key randomly

Views:362,Comments:0,Saved by 1 Sept. 7, 2008, 3:55 a.m. | spellscroll

A man has n keys of which one will open his lock and the others will not. If he tries the key randomly one at a time, what is the ...

Tags: probability(1)

Circle-Circle Tangents

Views:695,Comments:2,Saved by 1 May 17, 2009, 2:51 a.m. | spellscroll

Given two circles with centers (x1,y1) and (x2,y2) and radii r1 and r2, write a program to find all lines tangent to these two circles.

Tags: geometry(1) circle(1)

连庄 vs. 轮庄

Views:760,Comments:3,Saved by 5 Oct. 22, 2008, 9:15 p.m. | spellscroll

两个赌徒A和B决定用如下规则开始赌博:
(1) 初始二人均为0分, 每局胜者得1分,先积满n=12分者为最后胜者.
(2) 另外每局需要挑选一人当庄, A当庄胜率为p=0.7, B当庄胜率为q=0.6.
有两种选庄规则, 一种是轮流当庄, 另一种是胜者连庄. 现在假设第一局由A当庄, 请问那种选庄规则对A更有利?

Tags: to_study(1)

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