What is the smallest number of people Mohhawk would need to have in a room if he wanted to be certain that at least 25 of them have the same birth month?
from Mathcounts Trainer
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Eu pensei inicialmente em 301, pela fórmula do 2 5 × 1 2 +1. Mas após raciocinar um pouco, lembrei do fato de que Mohhawk sabia seu aniversário, não precisando de pessoas para preencher 12 meses. Ou seja, a fórmula final é 2 4 × 1 2 +1.
OBS: O nome dessa matéria é "Princípio das casas dos pombos", caso queira estudá-la.
Initially, I thought in 301, by using 2 5 × 1 2 +1. But this wasn't right, then I remembered that Mohhawk already knew his birthday. So he didn't need 12 people, only himself. So it's not 2 5 × 1 2 +1, but 2 5 × 1 2 +1-12, which is equal to 2 4 × 1 2 +1.
1 year has 12 months. If 12 people have different birth months, the 13rd person WILL CERTAINLY fit one of the twelve months [of a year]. So you need 12x+1 people to be certain that at least x of them have the same birth month.
*PS: The image don't have Mohhawk represented. He is the (+1). Each box represents one month and each month has 24 dots. To have 25, you you need one more person (Mohhawk).