Twelve Crayons



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There are several possible ways to solve the puzzle. 

Way 1. Making just plain figures like in Solutions 1, 2, and 5 below.

Way 2. Less obvious. You have to make your starting and finish shapes 3-dimensional. One of the most "classic" solutions is based on placing 9 crayons (which have to form the final shape with 3 squares) along edges of a cube without one corner - you need exactly 9 crayons for this. This shape has exactly 3 perfect squares.

Solutions 4 and 6 use this principle. Solution 6 describes how to build the final shape. 

Way 3. Using crayons to form digits/numbers like in Solution 3.

We show all the six winning solutions.

Remove crayons a, b and c

Solution 1 by Nicole Takahashi

Twelve Crayons - Solution 1 by Nicole Takahashi

I would have had a hard time describing a soln to the twelve crayons, so I drew a picture (attached)*.

* Nice drawings Nicole! Thank you!

Solution 2 by Joao Paulo

Twelve Crayons - Solution 2 by Joao Paulo
Remove the red ones
Interesting puzzle I think the answer is correct 
Thank you for the great site

Solution 3 by Jensen Lai

Arrange 12 crayons into 4 lines with 3 crayons in each line. This yields the numbers 1, 1, 1, and 1. Each is a perfect square. Take away three crayons and you are left with 1,1 and 1. Thus, you are left with 3 perfect squares.

Solution 4 by Alex Packard

Arranging twelve matchsticks to give four perfect squares.

I cannot show this on a picture but it is a front square, a top square, a side square, and a square adjacent to the side square. This configuration is similar to a box with no bottom and missing one side. This box has a 'lid' - the square adjacent to the side square.

Another way to put it is a die with two sides removed, and one more side flipped up; keep that side intact.

Removing the three crayons which comprise the 'lid' of the box (or the flipped up part that is not an integral part of the three sided die), leaves only 3 perfect squares left.

Solution 5 by Federico Bribiesca Argomedo

If we consider the following figure:

Twelve Crayons - Solution 5 by Federico Bribiesca Argomedo

It's marking four different perfect squares with twelve crayons, if we remove the three crayons outside the 2x1 rectangle, we'll have three perfect squares and nine crayons, so we've accomplished our goal.

Solution 6 by Jeffrey Czarnowski

Set the match sticks up in a cube. Then remove any three sticks that are perpendicular to each other (i.e. remove a corner).

Last Updated: July 8, 2007  |  Posted: January 24, 2002
PDF Version (185 KB)

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