Question: Marbles in a bag example: The theorem states that in any bag of black and white marbles all the marbles are the' same color. The proof by induction starts with the case of a bag with one marble. Certainly all the marbles in the bag are of the same color. Next we assume the theorem is true for any bag of m marbles. Take a bag with m + 1 marbles and remove one. By the induction hypothesis, they are all of the same color. Replace it and remove another marble. Again they are all of the same color. Thus all the marbles in the bag are of the same color.