Problem #1 – Mind-Meld Mazes: Words, Colors, Numbers

 

PRACTICE. Emily has 2 red, 3 blue, and 1 green crayon in a box. She closes her eyes and pulls out two crayons at the same time.

  1. List every color pair she might pull.

  2. How many different pairs are possible?

Blindfolded girl-figurine holding a red and a blue crayon – graphic for a combinatorics problem about drawing crayons at random
Red–blue crayon pair equals blue–red pair — illustration for BrainSpark combinatorics task (order doesn’t matter).

Remember: the order doesn’t matter; “red + blue” is the same pair as “blue + red.”

Gray box of crayons for a counting-and-combinatorics problem: 2 red, 3 blue, 1 green.

Clue:
We have six small crayons—2 red, 3 blue, and 1 green.
• First, see if Emily can pull two crayons of the same color.
• Then think of every possible mixed-color pair and color those pairs on your drawing.

Solution

Unique color pairs

  • RR (two reds)

  • BB (two blues)

  • RB (red + blue)

  • RG (red + green)

  • BG (blue + green)

Answer: Emily can end up with five different color pairs.

Why Learning to Choose Wisely Matters

This little “crayon-in-a-box” puzzle is a child’s first step into combinatorics—the branch of math that underpins discrete mathematics and probability. By figuring out how many color pairs Emily can pull, kids practice:

  • counting possibilities in a structured, efficient way;
  • seeing the hidden setup of a problem (2 reds, 3 blues, 1 green);
  • using the same skill set in real life—whether picking menu items or judging password strength.

Being able to list and compare all combinations is a powerful habit for logical thinking and everyday decision making.

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