# Inspired from similar ones

**Discrete Mathematics**Level 3

1000 people are standing in a circle . Every person has a number on his shirt (starting from 1 to 1000) and are standing consecutively according to the numbers ( person 1 is next to 2 and person 2 is between 1 and 3 and so on , also , person 1000 is between 1 and 999) . If person 1 has a sword in his hand and he kills person 2 and 3 and passes the sword to 4 and then person 4 kills person 5 and 6 and passes the sword to 7 and so on. Who will be the lucky man/men who is/are alive whereas all others will die ?

Note: 1.)If two persons are left they cannot kill anyone as they one has to kill compulsarily two people.

2.)If at last only one person is left then give the answer as the number of the person and If at last two are left submit your answer as the sum of numbers they are having.