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Omni-MATH / Morteza and Amir Reza play the following game. First each of them independently…

Problem

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problem

Morteza and Amir Reza play the following game. First each of them independently roll a dice 100100 times in a row to construct a 100100-digit number with digits 1,2,3,4,5,61,2,3,4,5,6 then they simultaneously shout a number from 11 to 100100 and write down the corresponding digit to the number other person shouted in their 100100 digit number. If both of the players write down 66 they both win otherwise they both loose. Do they have a strategy with wining chance more than 136\frac{1}{36}?
Plain-text mathematical notation (without MathML)
Morteza and Amir Reza play the following game. First each of them independently roll a dice 100 times in a row to construct a 100-digit number with digits 1,2,3,4,5,6 then they simultaneously shout a number from 1 to 100 and write down the corresponding digit to the number other person shouted in their 100 digit number. If both of the players write down 6 they both win otherwise they both loose. Do they have a strategy with wining chance more than (1)/(36)?
Original LaTeX notation
Morteza and Amir Reza play the following game. First each of them independently roll a dice $100$ times in a row to construct a $100$-digit number with digits $1,2,3,4,5,6$ then they simultaneously shout a number from $1$ to $100$ and write down the corresponding digit to the number other person shouted in their $100$ digit number. If both of the players write down $6$ they both win otherwise they both loose. Do they have a strategy with wining chance more than $\frac{1}{36}$?

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Source and history

task_id
97c93180-3285-5964-8960-bfd059c83afd
task_key
test--97c93180-3285-5964-8960-bfd059c83afd
task_revision_id
1
config / split
/ test

Official source

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