## A hundred people participated in a flash mob. First, they formed a circle. MJ marked as number one had a torch. He pointed the to

Question

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?

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Mathematics
2 years
2021-07-15T14:20:18+00:00
2021-07-15T14:20:18+00:00 2 Answers
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## Answers ( )

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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Solution:–Case 1):-Conclusion:-So,

Left People are :- 1, 3, 5 , 7, 9, 11 , ____________ 99 .

Case 2):-So,

Left People are :- 1, 5, 9 , 13, 17, 21 , ____________ 97 .

Case3):-So,

Left People are :- 1, 9, 17 , 25, _______ 89 ,97 .

Case 4):-So,

Left People are :- 9, 25, 41, 57, 73, 89 .

Case 5):-So,

Left People are :- 9, 41, 73 .

Case 6):-therefore, In the end left people are 9 and 73 . now, the torch is in the hand of 73 . Since they are in circle,

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