OlympiadHardLogic7–9

A jar holds $20$ white balls and $16$ black balls. Two balls are drawn at random: if they have the same colour a black ball is put in, and if they have different colours the white one is put back. This is repeated until one ball is left. What colour is it?

Um frasco tem $20$ bolas brancas e $16$ bolas pretas. Retiram-se duas bolas ao acaso: se forem da mesma cor coloca-se uma bola preta, e se forem de cores diferentes devolve-se a branca. Repete-se até restar uma bola. De que cor é?

Answer options

Solution

Step 1 of 3

1.Follow the number of white balls. Two whites drawn: it drops by $2$ . Two blacks drawn: it does not change. One of each: the white returns, so it does not change either.

A jar holds 202020 white balls and 161616 black balls. Two balls are drawn at random: if they have the same colour a black ball is put in, and if they have different colours the white one is put back. This is repeated until one ball is left. What colour is it?

Answer options

A jar holds $20$ white balls and $16$ black balls. Two balls are drawn at random: if they have the same colour a black ball is put in, and if they have different colours the white one is put back. This is repeated until one ball is left. What colour is it?