Y by MR.1, xytunghoanh, Leman_Nabiyeva, Exponent11, Nuran2010
Alice and Bob take turns taking balloons from a box containing infinitely many balloons. In the first turn, Alice takes
amount of balloons, where
. Then, on his first turn, Bob takes
amount of ballons where
. After first turn, Alice and Bob alternately takes as many balloons as his/her partner has. Is it possible for Bob to take
amount of balloons at first, such that after a finite amount of turns, one of them have a number of balloons that is a multiple of
?






This post has been edited 1 time. Last edited by Sadigly, May 9, 2025, 7:50 AM