MathDB

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 ``+": 6965 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?

Problem Statement