100 people standing in a circle in an order 1 to 100.

No.1 person has a sword.

He kills next person (i.e. No. 2 )and gives sword to next to next (i.e no.3).

All person does the same until only 1 survives.

Which number survives at the last?

+2 votes

100 people standing in a circle in an order 1 to 100.

No.1 person has a sword.

He kills next person (i.e. No. 2 )and gives sword to next to next (i.e no.3).

All person does the same until only 1 survives.

Which number survives at the last?

+2 votes

Answering on Behalf of Chaturbhuj Kuntal

**73 is the answer....**

As long as the number is power of 2, the person survived will always be the one who starts. If the number is not power of 2, find the greatest power of 2 which is less than the number i.e. 64 now if 100-64=36 people are killed, the one who will start after that would be the one who will survive.

36 people will be killed as 2,4,6, .... ,72 and the sword will be handed over to 73 who is the first person to start in remaining 64. thus only 73 will survive.

+2 votes

Answer is 73.The formula to find the no. that will survive in a list (of numbers) is as below:

If the total count of the list is in exponents of 2, then it’s the 1st no. will survive.

If the total count is not an exponent of 2, then subtract the total count from the next exponent of 2. If you call the result as ‘x’, then the number that survives is the xth number of the list counted backwards.

+1 vote

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(got sword, passed to 1)

den 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(sword passed to again)

den 1,9,17,25,33,41,49,57,65,73,81,89,97(sword passed to 9)

den

9,25,41,57,73,89(sword passed to 9 again) den

9,41,73(sword passed to 9 again)

den 9,73(73got sword & killed d 9)

soo answer s "73"

ACN ans....73....

Soldiers are standing in a circle.

That means in second round 99 will kill 1instead of passing knife from 99 to 1.

I ended with 31 with the above logic.

That means in second round 99 will kill 1instead of passing knife from 99 to 1.

I ended with 31 with the above logic.

Wrong as it said it goes circle in circle so continuous loop it is, therefore 99 doesn't passes it to 1 instead it kills 1.

And the answer comes out to be 29

And the answer comes out to be 29

+1 vote

The answer is 73.

```
$numbers = range(1,100); //define an array with 100 elements starting from 1 to 100
$round = 1; //define a variable to keep note of how many rounds are required to get the answer (this is optional)
$temp = 1; //Just a Boolean variable to remove alternate element
//As removing elements from array will be repetitive task we define a function which will remove elements.
function remove_elements(){
global $numbers, $round, $temp; //Use the variables inside function by defining them global
foreach($numbers as $key=>$value){ //iterate the loop for each element of an array
if($temp == 0) {
unset($numbers[$key]); //remove alternate element
$temp = 1;
}
else {
$temp =0;
}
}
echo "Round $round: ".implode(', ',$numbers)."<br>"; //print the round number and elements remained after removing elements in that round
$round++; //increase the round number for each iteration
if(count($numbers) != 1){
remove_elements(); //we are calling remove_elements function recursively until we are left with only one element in our array
}
}
remove_elements(); //Call the function
```

Output of this program would be as below:

```
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
```

Check out the detailed description on blog to solve it using programming. http://www.mittalpatel.co.in/solving_puzzle_with_programming

0 votes

Daman Malhotra and Salil Agrawal has given good answers; i'm just trying to complete what they said.

It's purely binary. Try your methods (pls everyone try their own methods; don't try to imitate sb else) on the following variants of it:

1) There were 109 mad men standing in a circle. Suddenly, the 1st man took a knife, killed the man on his right (ie, 2nd man) and passed the knife to the next (ie, 3rd man). The 3rd man did the same. This went on until only 3 were left. Then just like the pattern, one man (say Bob) killed the man on his right and passed the knife to other man. But when the other man tried to kill him, he(Bob) got angry, managed to snatch the knife from the other man and killed him too. What was Bob's position?

2) Roughly 150 mad men standing in a circle performs the same 'ritual'. At last only 79th man survived. Exactly how many were there when they stated?

If you have solved these try the last one I have to offer:

*3) There were 61 mad men standing in a circle. Suddenly, the 1st man took a knife, killed the man on his right (ie, 2nd man) and passed the knife to the next (ie, 3rd man). The 3rd man did the same. This went on for one cycle after which the man with the knife in his hand killed the man on his left and passed the knife to the next man on his left. This went on for that cycle. Like this, quite a number of cycles were done each cycle changing direction at the start of the cycle? After all, all one survived. What was the survivor's position?

(a clarification on 3rd question - this means, each mad man upon getting the knife first time kills and passes knife to the right and when he gets the knife a second time kills and passes the knife to the left. If we gets it a 3rd time, he will go for right again. For 4th time, left and so on.)

0 votes

We can solve this puzzle be recursive and non recursive method.here Think just greater then the number exact power of 2 from n.after then-

survive number=1-2^x+2n

Ex- If there is 100 person and no.1 has a sword then

survive no.=1–2^7+2(100)

=73(ans).

Ex- If there is 1000 person and no.1 has a sword then

survive no.=1–2^10+2(1000)

=977(ans).

if no.2 has a swoed then

survive no=2–2^10+2(1000)

=978(ans).

...