MathDB
Problems
Contests
International Contests
Iranian Combinatorics Olympiad
2020 Iranian Combinatorics Olympiad
2
2
Part of
2020 Iranian Combinatorics Olympiad
Problems
(1)
Strategy for Higher Winning Probability
Source: Iranian Combinatorics Olympiad 2020 P2
4/22/2020
Morteza and Amir Reza play the following game. First each of them independently roll a dice
100
100
100
times in a row to construct a
100
100
100
-digit number with digits
1
,
2
,
3
,
4
,
5
,
6
1,2,3,4,5,6
1
,
2
,
3
,
4
,
5
,
6
then they simultaneously shout a number from
1
1
1
to
100
100
100
and write down the corresponding digit to the number other person shouted in their
100
100
100
digit number. If both of the players write down
6
6
6
they both win otherwise they both loose. Do they have a strategy with wining chance more than
1
36
\frac{1}{36}
36
1
?Proposed by Morteza Saghafian
combinatorics
probability