Sunday Times Teaser 3275 – Against the Odds
by Andrew Skidmore
Published Sunday June 29 2025 (link)
I have taken a number of playing cards (more red than black) from a standard pack of 52 cards and distributed them in a certain way in two piles, each containing both red and black cards.
A card is taken at random from the smaller pile and placed in the larger pile. The larger pile is shuffled; a card is taken at random from it and placed in the smaller pile.
There is a one in eight chance that the number of red and black cards in each pile will be the same as they were originally.
How many black cards in total were used?
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Only six r1 iterations.
Here is my analytically based solution: