Math Puzzle: Tricky calculation

Using only the numbers 1, 2, 3, 4, 5 and 6 and the mathematical operations addition, subtraction, multiplication and division, can you arrive at the value 456? You may use each number at most once in your full solution, and parentheses are permitted.

There are many solutions to this problem. Here’s one:

3 × (6 + 2) × (4 × 5 – 1)

Breaking that calculation down, you get

6 + 2 = 8
8 × 3 = 24
5 × 4 = 20
20 – 1 = 19
24 × 19 = 456

Bonus challenge: What is the closest you can get to 456 if you are required to use division? What if you are required to use all the operations?

We’d love to hear from you! E-mail us at games@sciam.com to share your experience.

Emma R. Hasson is Scientific American’s Games ace and a Ph.D. candidate in mathematics at the City University of New York Graduate Center with expertise in math education and communication. Hasson was also a 2025 AAAS Mass Media Fellow at Scientific American.

More by Emma R. Hasson