« Vrati se
Three persons A,B,C, are playing the following game:

A k-element subset of the set \{1, . . . , 1986\} is randomly chosen, with an equal probability of each choice, where k is a fixed positive integer less than or equal to 1986. The winner is A,B or C, respectively, if the sum of the chosen numbers leaves a remainder of 0, 1, or 2 when divided by 3.

For what values of k is this game a fair one? (A game is fair if the three outcomes are equally probable.)

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
1669IMO Shortlist 1986 problem 60
1667IMO Shortlist 1986 problem 40
1355IMO Shortlist 1969 problem 250
1354IMO Shortlist 1969 problem 240
1353IMO Shortlist 1969 problem 230
1348IMO Shortlist 1969 problem 180