hard math question

[Mirage2000]

<p>There are 6 red, 6 brown, 6 yellow, and 6 gray scarves packaged in 24 identical, unmarked boxes, 1 scarf per box. What is the least number of boxes that must be selected in order to be sure that among the boxes selected 3 or more contain scarves of the same color?</p>

[Mirage2000]

<p>never mind</p>

<p>

The problem basically says, how many scarves must we pick to have a 100% chance of there being 3 or more of the same color. All we have to do to disprove an answer choice is give a scenario in which there are 2 or less of the same color, based on the number of scarves we’re choosing.</p>

<p>3 scarves
We could have 1 red, 1 brown, 1 yellow scarf so A is wrong</p>

<p>6 scarves
We could have 2 red, 2 brown, 1 yellow, 1 gray so B is wrong</p>

<p>7 scarves
We could have 2 red, 2 brown, 2 yellow, 1 gray so C is wrong</p>

<p>8 scarves
We could have 2 red, 2 brown, 2 yellow, 2 gray so D is wrong</p>

<p>E is left as the correct answer. Even if we tried to minimize the number of repeating colors, at best we’d have 3 of the same color and 2 each of the rest (3+2+2+2 =9).

</p>

[SATwriter]

<p>An easier way to think about this question is to figure out how many scarves you have to select to have 2 of every color:</p>

<p>2 red + 2 brown + 2 yellow + 2 gray = 8 boxes. </p>

<p>The next box you pick, the 9th one, whether it is red, brown, yellow, or gray, will make 3 of the same color.</p>