# Measure the diagonal of a brick

You are given three identical bricks (cuboids) and a ruler (scale) as shown in the figure. You have to find the length of the brick's diagonal without using any formula and by using the ruler only once. How will you do it?

(You can't break or change any physical properties of the material provided and you can't use your own material. There is no unique answer to this puzzle, and various solutions may be found useful.)

• While your questions are generally well-received, you have not made an attempt to choose a correct answer. It would only be fair to the answerers if you chose the best answer as the correct answer by clicking on the small tick below the answer you like. Thank you! Aug 16, 2015 at 16:59
• When you say "using scale only once" do you mean "measuring only once"? Aug 17, 2015 at 14:00
• Yes exactly that. Aug 22, 2015 at 2:57

Align all the bricks in the same orientation and put them together in an L shape like this:

brick
brickbrick


Then the body diagonal can be measured in the "missing fourth brick" directly, unobscured by material.

• Much better solution than mine. Aug 16, 2015 at 18:11
• good one. +1 for simplicity Aug 17, 2015 at 9:34
• Simple,Well Explained and absolutely right. Aug 22, 2015 at 2:58

This can be measured directly and easily as shown.

• +1 for the nice illustration, but it is identical to Vašeks answer. Aug 16, 2015 at 16:51
• @CarlLöndahl - Ah yes I see. Please feel free to give my upvotes to Vašek Potoček. Aug 16, 2015 at 18:24
• great chasly. +1 for decoration Aug 17, 2015 at 9:34

The (twice) given geometrical answer is very clever.

Here's a much less clever solution, using very basic engineering only. It utilises the fact that the diagonal happens to be the longest dimension of the brick.

Stand two of the bricks up on the ground with some room in between. Keeping one corner always touching one brick,

use the third brick to push the other brick as far away as possible.

Like so:

Now you can easily measure the distance between the two bricks.

To make the measurement more accurate, you can add markings on the two bricks, and only push the marked spots away from each other.

Make sure the first brick's longest two edges face upwards. Then put the other two on top of it so that they're congruent to each other, with the other edge also on the bottom and adjust them until the longest edges of both will form the diagonal with some of the length left over (hold/support the top bricks to stop them falling off if necessary). Finally measure the distance between the point where the leftover begins and the opposite corner on the other top brick.

If holding/supporting them is illegal, you can put the two "top bricks" first, put the first one mentioned on top, adjust it and measure. Pic below:

• You really want to explain it better, I only understood (read deciphered) it after reading it 15 times. The pictures don't help much either. Aug 17, 2015 at 11:56