A probability problem by Swadesh Rath

Probability Level 4

There are four basket-ball players A, B, C, D. Initially, the ball is with A. The ball is always passed from one person to a different person. In how many ways can the ball come back to A after seven passes? (For example A → C → B → D → A → B → C → A and A → D → A → D → C → A → B → A are two ways in which the ball can come back to A after seven passes.)


The answer is 546.

Swadesh Rath by Swadesh Rath , 25, India

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2 solutions

Saharsh Rathi
Oct 31, 2016

I started from the 7th pass and kept making all the cases backwards .

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Bill Bell
Nov 9, 2015

Not only do I know how many there are I can say what they are. (Not that that matters.) 

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from copy import copy

def build(chain):
    global count
    end=chain[-1]
    possibleLinks='ABCD'.replace(end,'')
    for nextLink in possibleLinks:
        if len(chain)==7:
            if nextLink=='A':
                print '%s%s' % (chain, nextLink)
                count+=1
            return
        elif len(chain)>6:
            return
        else:
            build(copy(chain)+nextLink)

count=0
build('A')

print count

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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