MathDB

Given 2015 balls. Astri and Budi will play a game. At first, Astri will choose two different numbers

a

and

b

from the set

S = \{ 1, 2, 3, \dots, 30 \}

. Budi will then choose another 2 different numbers

c

and

d

from the remaining 28 numbers in set

S

.
By taking turns, starting from Astri, they take balls with the following rules: (1) Astri could only take

a

b

balls. (2) Budi could only take

c

d

balls. until someone couldn't take any balls satisfying the condition given (and that person will lose).
Prove that Budi could choose

c,d

such that he has a strategy to ensure his victory on this game.

C9