The optimal sacrifice!
A very intelligent and kind traveller is caught by a king and made to prove his wit. The king suggests a game, the victory to which would affirm his intellect and guarantee his freedom. The game is : 'N' people stand in a circle and one of them has a sword. The rule is to slice off the person next to you (the starting player) and pass the sword to the next in order who slices his next and passes the sword. The game continues untill only one survives and is declared the winner. The twist is that the traveller is made to stand at the 489th position and is given the liberty to add as many people he likes after him and also choose the starting position for the game. Note : he is kind, so he must choose the minimum number for the kills and thus 'the optimal sacrifice'.
If the traveller chooses 'm' number of people after him and 'n' as the starting position and wins out alive, then what is m+n?
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
The problem is similar to the 'Josephus problem'. You must check it out too.
A careful observation reveals that for 1 being the starting position, powers of 2 lead to the victory of the player in the 1st position. So the nearest the traveller could get to saving lives as well as staying alive in the same hand is if he chooses to start the game (hence the 1st position) and adds 23 people after him (for the nearest power of 2).