SOCK DRAWER PUZZLE

Math Teasers are meant for thinking outside of the box. They require more logical thinking than being a math whiz-kid.  Today you are presented with the Sock Drawer Puzzle.

SOCK DRAWER PUZZLE

Your sock drawer contains

15 green socks and

15 blue socks.

Without looking, what is the smallest

number of socks you need to take out

to guarantee a matching pair?

Answer: 3.

If the first two don’t match, the third one will certainly match one of the first two.

THE PIGEONHOLE PRINCIPLE

These riddles, often called “pigeonhole principle” puzzles, focus on ensuring a result in a “worst-case scenario.” They require finding the minimum number of items to guarantee a match, similar to the 3-sock rule (two colors = three socks).

• 

  The Mixed Drawer: You have 10 red, 8 blue, 6 green, 4 orange, and 2 white socks in a dark drawer. How many must you pick to guarantee one matching pair? (Answer: 6, as you could pick one of each color, then the 6th must match).

• The Triple Color Drawer: You have 12 red, 12 white, and 12 black socks. How many to guarantee a pair? (Answer: 4).
• The Specific Pair Challenge: You have 53 socks: 21 blue, 15 black, and 17 red. How many to ensure a black pair? (Answer: 40—you could pull all red, all blue, and then need two more to get the two black socks you wanted).
• The Shoe Problem: In a room, there are 34 shoes (17 pairs). How many must you take to guarantee you have one full pair? (Answer: 18).

Key logic: Always count the maximum number of socks you can pull without making a pair (one of each color), and then add one more. 

Are you ready to challenge your math mind? Sign up for class(es) at MyTutorLesson – Math.