MathDB

Pedro and Juan are playing the following game:

-

There are

2

piles of rocks, with

X

rocks in one pile and

Y

rocks in the other pile (

X < 12, Y < 11

-

Each player can draw: --

1

rock from one of the piles, or --

2

rocks from one of the piles, or --

1

rock from each pile, or --

2

rock from one pile and

1

from the other pile. Each player must perform one of these four operations in their turns. The looser is the one who takes the last rock. Pedro plays first and has a winning strategy. What are the three maximum possible values of (

X+Y

Problem Statement