13 white marbles and 15 black marbles

Question:

In a box you have 13 white marbles and 15 black marbles. You also have 28 black marbles outside the box. Remove 2 marbles, randomly, from the box. If the marbles are of different colors, put the white one back in the box. If they are of the same color, remove both of them and replace them with a black marble from outside the box. Continue this process until only 1 marble remains in the box. What color is the last marble?

.

.

C

A

P

T

A

I

N

I

N

T

E

R

V

I

E

W

.

.

Solution: Some interviewers prefer candidates who solve this problem intuitively as opposed to the brute force method other candidates use. One interviewer thought this candidate’s response was ideal:

Since marbles can only be taken out in pairs and we started off with an odd number of white marbles, there is always going to be 1 white marble left over that you’ll keep putting back in the box until it’s left on its own.

Solution: The last marble will be white.

 

 

 

 

 

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