A hundred people participated in a flash mob. First, they formed a circle. MJ marked as number one had a torch. He pointed the torch at the person next to him, Ravi, and passed the torch to the person marked as third. Meanwhile, Ravi walked away from the circle. The passing of the torch and the walking away from the circle continued till only one dancer remained. What’s the number of the last dancer?
Given : A hundred people participated in a flash mob. First, they formed a circle. MJ marked as number one had a torch. He pointed the torch at the person next to him, Ravi, and passed the torch to the person marked as third. Meanwhile, Ravi walked away from the circle. The passing of the torch and the walking away from the circle continued till only one dancer remained.
To Find : number of the last dancer
a) 88
b) 78
c) 85
d) 73
Solution:
cycle 1
walk away 2 4 6 8 10 _____________ 98 100
remaining 1 3 5 7 9 _________ 97 99
Cycle 2 :
walk away 3 7 11 15 _________ 95 , 99
remaining 1 5 9 _______ 93 , 97
Cycle 3
walk away 5 13 21 _______ 93
Remaining 1 9 _____ 89 , 97
Cycle 4
walk away 1 17 33 49 65 81 97
remaining 9 25 41 57 73 89
Cycle 5
walk away 25 57 89
Remaining 9 41 73
Cycle 6
walk away 41
Remaining 9 73
Cycle 7
Walk away 9
Remaining 73
Hence dancer number 73 is remaining
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