Further and deeper exploration of paradoxes and challenges of intuition and logic can be found in my recently published book, Probability, Choice and Reason.

You are presented with four cards, with the face-up side on display, showing either a letter or a number. You are promised that each has a letter on one side and a number on the other.

Red Card displays the letter D

Orange Card displays the letter N

Blue Card displays the number 21

Yellow Card displays the number 16

You are now presented with the following statement: Every card with D on one side has 21 on the other side.

Exercise

a. What is the minimum number of cards needed to determine whether this statement is true? What are the colours of the cards you need to turn over to determine this?

b. Four cards are placed on a table, each of which has a number on one side and a patch of colour on the other side. The visible faces of the cards display 1, 4, red and yellow. What is the minimum number of cards you need to turn over to test the truth of the proposition that a card with an even number on one face is red on the other side?

3. Four cards are placed on a table, two of which display a number, 16 or 25. The other two cards display a soft drink and an alcoholic drink. The minimum age for drinking alcohol is 18. What is the minimum number of cards you need to turn over to test the truth of the proposition that a card with a number greater than 18 on one side has an alcoholic drink on the other side?