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Omni-MATH / The digits of a calculator (with the exception of 0) are shown in the form…

Problem

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problem

The digits of a calculator (with the exception of 0) are shown in the form indicated by the figure below, where there is also a button ``+": [img]6965[/img] Two players AA and BB play in the following manner: AA turns on the calculator and presses a digit, and then presses the button ``+". AA passes the calculator to BB, which presses a digit in the same row or column with the one pressed by AA that is not the same as the last one pressed by AA; and then presses + and returns the calculator to AA, repeating the operation in this manner successively. The first player that reaches or exceeds the sum of 31 loses the game. Which of the two players have a winning strategy and what is it?
Plain-text mathematical notation (without MathML)
The digits of a calculator (with the exception of 0) are shown in the form indicated by the figure below, where there is also a button ``+":
[img]6965[/img]
Two players A and B play in the following manner: A turns on the calculator and presses a digit, and then presses the button ``+". A passes the calculator to B, which presses a digit in the same row or column with the one pressed by A that is not the same as the last one pressed by A; and then presses + and returns the calculator to A, repeating the operation in this manner successively. The first player that reaches or exceeds the sum of 31 loses the game. Which of the two players have a winning strategy and what is it?
Original LaTeX notation
The digits of a calculator (with the exception of 0) are shown in the form indicated by the figure below, where there is also a button ``+":
[img]6965[/img]
Two players $A$ and $B$ play in the following manner: $A$ turns on the calculator and presses a digit, and then presses the button ``+". $A$ passes the calculator to $B$, which presses a digit in the same row or column with the one pressed by $A$ that is not the same as the last one pressed by $A$; and then presses + and returns the calculator to $A$, repeating the operation in this manner successively. The first player that reaches or exceeds the sum of 31 loses the game. Which of the two players have a winning strategy and what is it?

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Source and history

task_id
e883d82b-5232-5c4a-8bbf-61486b1656c1
task_key
test--e883d82b-5232-5c4a-8bbf-61486b1656c1
task_revision_id
1
config / split
/ test

Official source

initial import