A and B play a game of ‘Dingo’ in which each player in his turn has to

My Answer: (D) 1535

My Approach: Options B,C and E can be eliminated right from the beginning since they do not fall under the conditions as described in the rules of the game.

We're given that the player who chooses 1 loses. So let's start from here.

if the player gets their turn at 2, then they lose because they can only choose 1. Therefore 2 is a losing position.

Now if we get our turn at 3 or 4 we can choose 2 and the other player would lose. Therefore, these are winning positions.

5 is the next losing position, since If we get our turn at 5, we can only select as low as 3 and the other player can select 2 and hand us a losing position.

so we see that 2,5,11 and so on are losing positions. the general formula comes out to be 2n+1 where n is also a losing position.

here, I just want to highlight the logic behind this generalisation, because that's the backbone of this approach.

LOGIC: if we want to hand over a losing position to the opposite player, we need to be within double of that number, otherwise we will not be able to hand over that position, as, according to the rules, the least number that we can select on our turn is half of the current number in play. We know that 2 is a losing position, therefore to hand over two we have to be within double of 2, i.e. 3 or 4, as soon as we are at 5, we can't hand over 2. This is the basis for the generalisation too.


the series looks like 2,5,11,23,47,95, 191, 383, 767, 1535 is a part of the series and thus (D) is our answer. If B selects 1535 which is greater than 2021/2 (and thus valid), then no matter what A selects, B will be able to handover a losing position to A and thus win the game.