Monday puzzle: the three brick problem

This is a fun geometric problem with a practical solution:

How can one measure the diagonal of a brick without any formula, using three bricks and a ruler?

Can you solve it? Give it a try before reading the answer below.


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The answer to the puzzle

There is a remarkably easy way to find the diagonal. What you do is place two bricks in a row, and then stack one brick on top of either one. So you have one brick, and then next to it two bricks, creating an empty space where a fourth brick could be placed.

Now measure the length of the diagonal on the empty space using a ruler. No Pythagorean theorem required!

Here’s a diagram to illustrate:



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  • jmhajek

    You should be able to do this with two bricks. Place the left one and the upper right one like they are in a figure, but lying on their side (when you look at the image, pretend the screen is the ground.) You can use the ruler to make sure the angle is right. 

  • Dan

    You can do this with one brick, with a little work.

    Take a brick (say the lower right in the figure) and place the ruler so it touches the lower left corner of the brick.  Then roll the brick “up” 90 degrees (now the brick is in the top right position in the figure)  The ruler already is at one point on the diagonal line; now put the ruler on the upper right corner of the brick that was moved and you have the desired measurement.

    The vantage point for these directions is looking “north” not looking “down” at the picture. 

  • Anonymous

    Or you could do this with one brick by putting the ruler directly on the diagonal.  There are some really convoluted solutions for something that you have the tools (ruler) to do with ease.

  • Anonymous

    Ignore that – I just re-read the description of the problem.  It’s Monday morning…

  • http://nickknowlson.com Nick Knowlson

    Could you elaborate? I still don’t see why you couldn’t just measure the diagonal of one brick.

  • Paul Smith

    …did you look at the diagram?

  • Paul Smith

    How would you guarantee that your two bricks meet at a 90° angle?

  • John

    The bricks give the right angle. All you need is a straight edge to line up the “top” of one with the “bottom” of the other, or the right of one with the left of the other!

  • http://nickknowlson.com Nick Knowlson

    Oh, I see it now. So yes, but obviously not close enough.

    At first glance it still looks like the diagonal along one side, but once I took a few seconds to verify what I was actually seeing it made sense.

  • Wormed7600

    that would measure the diagonal across a side, not the diagonal across the internal diagonal

  • Guest

    The diagonal runs right through the brick!

  • Jesse Galef

    With the ruler, we can measure the outside diagonals (along one side of the brick.) 

    With the solution Presh gave, we can measure the 3-D diagonal between the furthest corners – right through the middle of the brick.  I wish I had a ruler that could do that, but most of mine have trouble measuring through solid brick.

  • jmhajek

    The ruler.

  • http://mathema-tricks.blogspot.com/ Mquaes

    Or can’t  you do this without any brick, at all? Try a little work.

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