if there are 100 people in a circle no 1 has gun he kills 2 and passes gun to third person and lastly one will remain what is his number
Answers
Solution: 73rd person will survive at last
Explanation:
Here, we can define an array with 100 elements with values from 1 to 100.
No.1 has a gun. He kills next person (i.e. no. 2) and gives gun to next to next (i.e no. 3).
We have taken array element as a person. 1st person kills the next. So, starting from 1, we’ll remove next element i.e. 2.
Then first person gives gun to next to next i.e. 3. That person will also kill next person and this continues. Means, in array, we need to start with 1 and remove the every other (alternate) element till 100. (all the even numbers will be removed and we’ll be left with odd numbers only in array).
Round 1: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99
Round 2: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97
Round 3: 1, 9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97
Round 4: 9, 25, 41, 57, 73, 89
Round 5: 9, 41, 73
Round 6: 9, 73
Round 7: 73
●calculation by general Logarithm,
Step 1 : For a given value of N, find the “Power of 2” immediately greater than N. Let’s call it P
Step 2 : Subtract N from (P-1). Lets call it M, i.e, M = (P-1)- N
Step 3 : Multiply M by 2. i.e M*2
Step 4 : Subtract M*2 from P-1. Let’s call it ans, i.e, ans = (P-1) – (M*2)
So, the person with number “73" will survive till last.