bonanova

I don't recall that I posted it. The way I first heard it, tho, the question gives the speed of the fly and asks how far it flew. This form hasn't been posted that I can tell. What intrigues me about this version is that ...

Working on it. I have a conjecture: If two pairs of circles are congruent the triangle is isosceles.

Baskaran has it.

It's an excellent puzzle. You can find some extended discussion of it here. To locate previous posts, enter key words in the search box -- upper right corner, just under your name. I found this link by entering the words "hats death row" I happened to remember that "death row" was in the title.

A procedure that permits different interpretations does not help. If the counterfeit coin is lighter, then it's on the lighter side. If it's heavier then it's on the heavier side. All you can conclude is that the counterfeit coin is on the balance scale. But since you're weighing all the coins, you already knew it was on the scale. So you've learned nothing.

I'm thinking the answer is different for rational and real numbers. Is your question purposely directed to rationals?

I think your formula is correct. Do you have a proof?

Regarding the linked article Regarding the new solution,

If E=mc2 and F=ma then you can say E/c2 = F/a but not much more. E+F has no meaning. You can't meaningfully add two things that are not measures of the same quantity, like the energy it takes to melt a gram of ice and the force it takes to type the letter F on your computer keyboard. Or the number, in dozens, of apples in basket A and the elapsed time, in centuries, since the oranges in basket B were picked. It would make as much sense to say that the knowledge contained in all the books of the world could be preserved in a single book comprising a string of all their first words then all their second words and so forth. In a way, it's all there in a single book, but the destruction of syntax and context destroys meaning and knowledge as well.

@ Mr. Dog, Toadman's puzzle is well stated. It needs no correction. Not that this point has anything to do with the puzzle, but a balance beam does in fact compare weight and not mass. How is 6-6 / 3-3 / 1-1 a solution?

Could be an answer, but not the one I had in mind.

The killing of what animal involves the spilling of one's own blood?

I think the OP is asking: "without any four of the pieces forming a square." And, be careful: its sides needn't be parallel to the edges of the board.

Hi Toadman, and welcome to the Den. Please use the search button to check whether a riddle may already have been posted on the site. This one has. The Guidelines button can be useful as well. Keep them coming, tho, the new ones. Thanks!

@DejMar, I agree, there are noninteger too: the time intervals the lamp spends in one or the other state: the "on" times plus the "off" times sum to 2 minutes. The lamp is "on" more than it's off, but we can determine these times without ambiguity. I would add these nonintegers are limited to the rationals, however, not the reals. Still,

I'd bet on the

Ah, Mr. Thompson's lamp has been dusted off and put through its paces. We can answer this question immediately upon discerning

Association holds for finite series. Infinite series converge only under certain conditions, which fail in this case. So it's not proper to give the series a value at all. But let's ignore that and call the series S anyway. Then what is S? Clearly it's 1/2:

Here's a quick response, that may be way off

I think your answer is right. Mine is overkill. Are you sure that

Looks like ...

Sketch a 4-sided figure on a sheet of paper. Use each of its sides as the side of an outward square and join the centers of opposite squares. At what angle do the two lines intersect?