Challenge the king
A king has servants. He ordered them to stand in a circle and numbered them from 1 to .
He gave to number 1 a sword and ordered him to kill the one next in number and pass the sword until only one left.
(1 kills 2 and passes to 3 and so on)
If the king has 34 servants, 67 servants and 102 servants, which servant will stay last in each of the possibilities?
The Answer will be the sum of all three
The answer is 89.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
If the total no. of servants are any power of 2 then the answer will be the 1st servant(because after every round the number of servants will be halved and therefore ultimately 1st servant will survive).
Therefore, basically we have to change the total no. of servants to a power of 2 and then the answer will be the first one of the remaining servants.
Taking the case of 34 servants- After 2 and 4 are dead.. sword is with 5 and remaining servants are 32(a power of 2) therefore the answer will be the first of the remaining servants i. e.. 5
Taking the case of 67 servants- After 2..4..6..are dead sword is with 7 and remaining servants are 64(a power of 2) therefore the answer will be the first of the remaining servants i. e.. 7
Taking the case of 102 servants- After 2..4..6....74..76 are dead sword is with 77 and remaining servants are 64(a power of 2) therefore the answer will be the first of the remaining servants i. e.. 77
Adding these: 5+7+77=89 which is the answer