Hi,

This is a thread to discuss some of your other favorite puzzles, riddles, brain teasers, armchair treasure hunts, etc.

To get started, here's an online puzzle hunt I've participated in before: Puzzlecrack. It's a week-long competition with clues given through the web page. Past competitions (and solutions) are still there for you to figure out.

Another similar one is Microsoft's College Puzzle Challenge.

Any other favorites?

-Klatuu

This is a thread to discuss some of your other favorite puzzles, riddles, brain teasers, armchair treasure hunts, etc.

To get started, here's an online puzzle hunt I've participated in before: Puzzlecrack. It's a week-long competition with clues given through the web page. Past competitions (and solutions) are still there for you to figure out.

Another similar one is Microsoft's College Puzzle Challenge.

Any other favorites?

-Klatuu

Well, if they give us the length of AC and AB, you can use AD = sqrt(AC^2 + AB^2), which will me probably the first thing a math student will think off, except they will lack information. Also, you can use trigonometric stuff, if they give us the angle of DAC (let's say it alpha), because cos alpha = AB/AD, so AD = AB / cos alpha (you can use also sen alpha = AC/AD), but you are lacking information again.

In that moment a math student will saw the problem, figure out, and jump out of the window.

EDIT: by the way, my whole reasoning was "they only give us one number, and it's for something that doesn't even have a name. The thing kinda look like a circle. I'm gonna say it's one so the answer is 20".

So out of curiosity, how do you actually know that AB? and AC? are the same length? Is it because of the right angles?

It's a Rectangle, thanks to the right angles. If you separate them with AD, you get two Square Triangles. AB has the same lenght than CD, and AC has the same lenght than BD. Since you have an Square Triangle, you can use the Pythagorean Theorem to figure out AD, which is the hypotenuse, by using AB (or CD) and BD (Or AC). So, it's something like this:

=> (AD^2) = (AB^2) + (BD^2)

=> AD = sqrt(AB^2 + BD^2)

By the way, there's a way to figure out AC and AB if you suppose those are equal. Of course, by knowing AD = 20.

There are quite a few specific locations, but the answer you're looking for is the north pole

Now I'm curious for the other few specific locations!

When I said AB? and AC? I meant the ones that don't have names. Like, [AE] (the one with B on its way) and [AF] (the one with C on its way).

To know that [AD]=[AF], you need to know that [AE]=[AF], don't you?

My question was, how do you do that?

EDIT: Here, I changed the picture to show what I mean.

In my new picture, A isn't the center of the circle anymore.

In this case, it's obvious, since I wanted to show you what I meant. But how do you know that in the first picture, A is the center? What is the way to calculate it? Surely when you're just looking it's easy to get it wrong if it's just off the center, right?

In a equation, I can't think in a way to do it.

In fact, you can say there's no actual answer (For lack of information), because we're just assuming it's a quarter of a Circle. If it were the quarter of a Elipse, for example, AE =/= AF and we're screwed, unless they also give us AE.

So, in typical Math fashion, I assume it's a Quarter of a Circle. If it's a quarter of a circle, by definition all the lines from the middle to the perimeter of the circle has the same lenght (Because that's the definition of the circle). (I think). Since AF is a line from the middle to the perimeter, and AD is also a line from the middle to the perimeter, then AF = AD.

You then solve it geometrical.