MathDB

Ana and Banana are playing a game. Initially, Ana secretly picks a number

1\leq A\leq 10^6

. In each subsequent turn of the game, Banana may pick a positive integer

B

, and Ana will reveal to him the most common digit in the product

A\cdot B

(written in decimal notation). In the case when at least two digits are tied for being the most common, Ana will reveal all of them to Banana. For example, if

A\cdot B=2022

, Ana will tell Banana that the digit

2

is the most common, while if

A\cdot B=5783783

, Ana will reveal that

3, 7

and

8

are the most common. Banana's goal is to determine with certainty the number

A

after some number of turns. Does he have a winning strategy?

Problem Statement