Petya takes black and red cards out of a bag and stacks them in two piles. It is forbidden to place a card on another card of the same color. The tenth and eleventh cards laid out by Petya are red, and the twenty-fifth is black. What color is the twenty-sixth card laid out?
Show that after a card with an odd number was placed, two cards of the same color ended up on top.

## Solution

Notice that the positions where two cards of the same color are on top and the positions where two cards of different colors are on top alternate. Since the 10th and 11th cards are red, after the 11th card was placed, two cards of the same color (red) were on top. Therefore, after the 25th card (and any card with an odd number) was placed, two cards of the same color were on top. Since the 25th card is black, the two top cards are black. Thus, the next, 26th card, can only be red (a red card can only be placed on a black card).

## Answer

Red.