Question by Summer Clouds - Discuss with MathYouLike

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21/09/2017 at 09:17

A bag contains identical sized balls of different colours : 10 red, 9 white, 7 yellow, 2 blue and 1 black. Without looking into the bag, Peter takes out the balls one by one from it. What is the least number of balls Peter must take out to ensure that at least 3 balls have the same colour?

List of answers

Dao Trong Luan 21/09/2017 at 09:28

Worst case is Peter take out 2 red balls, 2 white balls, 2 yellow balls, all blue ball and black ball.

So Peter taken:

2 + 2 + 2 + 2 + 1 = 9 [balls]

Not three members of the same color, have to take 1 ball more

Number of balls to take are: 9 + 1 = 10 [balls]

Answer 10 balls
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Vũ Trung Dũng 30/09/2017 at 18:08

$A = x^{2} - x y + y^{2} > x^{2} - x y - x y + y^{2}$

$\Rightarrow A > x^{2} - 2 x y + y^{2}$

$\Rightarrow A > {(x - y)}^{2}$

But ${(x - y)}^{2} \geq 0$

$\Leftrightarrow A \geq 0$

But $A \neq 0 \Rightarrow A > 0$

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