Why Beauty Is Genius

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– Why are you called Geniusbeauty? I see you’re beautiful, but why “Genius“? I’ve got a riddle for you, so if you solve it, you will prove me, that you are the real Geniusbeauty. Here is a heap of bricks. I’ll give you a slide rule and you will have to measure the diagonal of the brick. But remember, that you can measure it only once!

In the end she proved, that she was not only beautiful, but also smart. How did she do this? What did she answer?

Please, if you want to find the solution yourself, do not look at the comments of this post, because someone could have already written it there. You will find the solution in the next brain game. You are always welcome to ask questions about the task, in case something is not clear. But sorry, I will not answer leading questions. Good luck!

The answer to the previous brain game is:

4 9 2
3 5 7
8 1 6

Every row, column and diagonal is 15. If you rotate the grid, the logic stays the same. For those, who would like to find out the logic in detail, here is the link: http://en.wikipedia.org/wiki/Magic_square.
Congratulations to those, who solved it: Stargoat, Chris, Steve, Hj, Laurentiu Craciunas, Jed Hawk! Many thanks to Jed Hawk for the detailed explanation.

1. Here’s my solution – you don’t need to post this, but I didn’t see
a link to email you rather than posting.

I assume by “heap” that there are at least three bricks. Create a
“mini-step” by putting one brick in front of you, and stacking two
bricks directly in back of it. Now measure from the top-front-left
corner of the first brick to the top-right-back corner of the top brick
of the two in the back. Essentially you are measuring the diagonal
of where a fourth brick would be if you had created two stacks of two bricks.

Alternate solution: If “measure once” means you are only allowed to use
the rule once (position it once), but can read off multiple numbers, there’s
another solution. Position three bricks next to each as in this ASCII diagram
(hopefully this won’t get clobbered in transmission), but without any gaps
between bricks. Basically from the width of the edge facing you
is different for each brick.

|—| |—–|
| | | |
———- | | | |
| | | | | |
———- |—| |—–|

Now place the ruler across the bottom, reading the numbers where each
brick ends. You can now compute the length of each edge, and use
the Pythagorean theorem to compute the diagonal. This isn’t as nice
a solution. Even though you’re placing the ruler once, reading
three numbers violates the spirit of “using” it once.

2. And how, darius, do you get the ruler through the brick to do that
measurement? Diagonal in this problem means front-left-top corner
to rear-right-back corner (or one of the other three equivalents), not
the diagonal of a face.

3. I’m thinking of using mirrors but can’t quite come up with what I want.
Mathematically, if the brick has dimensions L, B and H. Then the length of the true diagonal is:
sqrt(L^2 + B^2 + H^2).
I need some way to organise the mirrors in a single plane, possibly on the same parallel plane as the base of the brick, that allows me to measure one line only.

Maybe, since the flat diagonal = L^2 + B^2 I could line that up against the H side, somehow. Thus only need the mirror for the Height of the brick but argh, I could be wrong anyway.

4. Want a hint Jed? If not, stop reading.

If the brick wasn’t there, you could easily measure its diagonal.

5. I didn’t read the word “heap” the first time rounds – oops, that’ll teach me. I assume that every brick is uniform then, from the same mould so to speak.

Well in that case you can rest two bricks and measure in one straight line, by positioning the height of the second brick to extend the flat diagonal of the base of the first brick.

A—-B
C—-D
E
F