These pretzels are making me…. Geometric

Mathematics Mar 09, 2017

Here’s a fun (and delicious!) set of puzzles for you to try, inspired by “The Moscow Puzzles.”

You’ll need a big bag of pretzel sticks (or other items of equal size, like matchsticks or straws).

Puzzle 1:

First, arrange 12 pretzels like this:

How many squares can you count in this picture? There are five — four small ones, and one big one.

Now try these puzzles. (Note: all pretzels in your arrangement must be part of a square.)

  1. Make 2 squares of different sizes by removing exactly 2 pretzels.
  2. Make 3 congruent squares by moving exactly 3 pretzels.
  3. Make 3 congruent squares by moving exactly 4 pretzels.
  4. Make 7 squares (they can be different sizes) by moving exactly 2 pretzels.
  5. Make 10 squares (they can be different sizes) by moving exactly 4 pretzels.

Did you find any solutions? Scroll down to the bottom to see some (but not all) of ours.

Warning: Peeking before you’ve tried it takes away all the fun!

Puzzle 2:

For an extra challenge, try some of these exercises with this 3 x 3 pretzel square:

  1. Make 2 congruent squares by moving exactly 12 pretzels.
  2. Make 1 large and 4 small squares by removing (or eating!) exactly 4 pretzels.
  3. Make 3 squares by removing 6 pretzels.
  4. Make 2 squares and 2 congruent, irregular hexagons by removing 6 pretzels.

Puzzle 3:

A big thanks to Andrew Crisp, a member of our content team, for this one. Start with this arrangement:

The challenge: Move exactly 2 pretzels to create exactly 4 squares of equal size.

What solutions can you think of to puzzles 2 & 3? We’re interested to see what you’ve come up with!

Tweet @mathspace your solutions to these puzzles or make up your own using #pretzelpuzzles. We’ll post our favorite ones.

Solutions to Puzzle 1:

  1. Make 2 squares of different sizes by removing exactly 2 pretzels.

2. Make 3 congruent squares by moving exactly 3 pretzels.

3. Make 3 congruent squares by moving exactly 4 pretzels.

4. Make 7 squares (they can be different sizes) by moving exactly 2 pretzels.

5. Make 10 squares (they can be different sizes) by moving exactly 4 pretzels.

Great! You've successfully subscribed.
Great! Next, complete checkout for full access.
Welcome back! You've successfully signed in.
Success! Your account is fully activated, you now have access to all content.