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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