Dice Bucket (Math Brainteaser)

[Otis]

Joe has a bucket containing 28 dice. He has one red die, two orange dice, three yellow dice, four green dice, five blue dice, six purple dice, and seven white dice. He draws the dice out of the bucket one at a time without replacement, and without looking at their colors. What is the minimum number of dice that Joe must draw to guarantee that he has removed at least four dice of the same color?

? ? ? ? ? ? ?

[imath]\;[/imath]

 

[JeffM]

Spoiler

Eighteen.

It is possible to draw 1 red, 2 orange, 3 yellow, 3 green, 3 blue, 3 purple, and 3 white in any order within the first 18 selections.

Of course, assuming my arithmetic is OK, Joe has a better than 99% probability that it will take fewer selections.

 

[PWC]

I think the 19th die will guarantee either 4 of Green, Blue, Purple or White but I agree with Jeffm that this is the very unlikely to happen

 

[Harry_the_cat]

Spoiler

19. Same reason as JeffM but needs one more to get the fourth.

 

[JeffM]

I think the 19th die will guarantee either 4 of Green, Blue, Purple or White but I agree with Jeffm that this is the very unlikely to happen

Of course, you are correct.