Can Your Students Solve the Famous Handshake Problem? (Grades 3-8)

It's always a good idea to mix up your instruction every now and then just to keep your kids on their toes.

And sharing today's fun math riddles and brain teasers like the Handshake Puzzle with your students is a great way to engage your students and incorporate some excitement into your upcoming lesson plans.


The Famous Handshake Problem

Here's the scenario:

If there are 20 people in a room and they each shake each other's hands once and only once, how many handshakes are there all together?

This challenge makes for a great warm-up or cool-down activity for sparking mathematical discussion and creative problem-solving at any grade level!

Click Here to Download Your Free Handshake Problem PDF Worksheet

It's always fun to see the variety of strategies (acting out, drawing diagrams, algebraic, etc) that your students will apply to try to solve this puzzle.

More Free Resources: Can You Students Solve These Super Mario Math Puzzles?


Handshake Problem: Solution

Answer: 19 + 18 + 17 + ... + 3 + 2 + 1 = 190 total handshakes

Wait! Do You Want More Fun Math Puzzles to Share with Your Kids??

This puzzle is a sample from my best-selling workbook 101 Math Challenges for Engaging Your Students in Grades 3-8.

The book is available as a PDF download and you can also get a hard copy on Amazon (Free Amazon Prime Shipping Included; pages are in black-and-white).


Do you want more free math activities and resources for grades 1-8 in your inbox every week? Subscribe to our mailing list here to get more free math goodies!

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By Anthony Persico

Anthony is the lead educator and founder of Mashup Math. He lives in Denver, Colorado and is also a YouTube for Education partner. Follow him on Twitter at @mashupmath.