The daily puzzle on another site:
So I figured out the volume of the box and I was trying to estimate how many pennies would fit in that volume. And I was thinking “This is an unusually difficult puzzle for this site and the answer is going to be very approximate. I bet it’s a trick question.”
Sure enough. Their answer:
Just one, after which it will no longer be empty!
To which I say “Bullshit.”
I say ‘bullshit’ too. A riddle is different from a trick question.
Definitely a trick question, similar to “How far can you run into a forest that’s two miles wide?”
Only past the first tree; after that, you’re running in the forest.
It’s not just a trick question, it’s a mangled version of a standard trick question format, since it does not account for simultaneous actions. (Ethilrist’s example is a better specimen of the type, for what that’s worth.) Very lame.
The original site doesn’t call it a riddle, at least, though even calling it a “puzzle” is crap.
Lateral thinking puzzles are still a type of puzzle. A simple math problem really wouldn’t be.
Though I agree this one is bad for the reasons stated.
Yes, exactly. This sort of riddle (“How many things can you put into an empty thing?”) only works for a situation where you have to put the things in sequentially, one at a time. Then the trick is that people will interpret the question as asking “How many things can you put in before the thing is full?” when what it’s actually, literally asking is, “How many things can you put in before the thing is no longer empty?” If properly set up, this results in a legitimate trick question. But the OP’s version is, I agree, bullshit.
Yes the given answer to the riddle is false for a multiple of reasons. Another objection not raised: how thick are the sides of the box? It may theoretically not even fit a single penny.
Also, an empty box has a vacuum and as soon as the box is opened to hold the penny it will no longer be empty as air rushes in to fill the box.
There are so many ways to be even more asinine about this “riddle” than even the original author was.
So…anyone game for actually answering it?
I’ll bite.
A US penny’s dimensions are 0.75 inches (19.05 mm) in diameter and 0.0598 inches (1.52 mm) in thickness. Assuming they are all done exactly to specs, and that the relief of the objects/lettering don’t make them thicker, then each penny. stacked perfectly on top of eacvh other, will take up the space equal to the volume of a rectangular prism with dimensions of .75, .75, and .0598.
Each stack would be 200 pennies tall, with .04 of an inch clearance at the top.
You can put them in a 13 x 13 matrix of stacks (so 13 x 13 x 200 = 33800), but since .75 doesn’t go in evenly into 10, there is a third of an inch left over for you to put in some sideways. Each third of an inch will allow sideways stacks with 5 pennies each, with 21 spaces available (10 one way, 10 the other, with an “extra” space in the corner). That’s 21 x 5 = 105 there.
Final tally: 33800 + 105 = 33905.
Feel free to critique.
Hexagonal packing of circles is more space-efficient than square packing. Here’s a calculator showing how many pennies will fit in the first layer: pack circles of radius 0.375 in a square of side 10 - Wolfram|Alpha
It gives a result of 191, so we have 191 stacks. Using your 200 pennies/stack, that gives us 38200.
Visual inspection of the packing pattern suggests that we may have 10 spots where additional pennies could be inserted on edge (along the edge and in the disordered area). 12 inches allows a stack of 16 pennies on edge, netting us another 160 pennies. (Maybe you could really cram the cracks by offsetting the on-edge pennies, but I’m not going to chase that.)
Final tally: 38200 at least, possibly up to ~38360.
It’s a riddle; the given answer is both fair and correct.
If it were a math problem, then the OP would have a fair complaint.
Nah, it’s still terrible. I could dump a handful of pennies in simultaneously and it would “no longer be empty!” with more than one penny. Or, if you’re a stickler about “placed”, I could carefully set in a column of pennies so all were “placed” when the bottom one touches the box.
So the “answer” isn’t just one. It’s not only a dumb and poorly phrased riddle, the answer isn’t even accurate.
The answer to the riddle could be “zero”, since placing any object in the box makes it no longer “empty” and this object doesn’t have to be a penny, or at least there’s no explicit requirement for such.
If Zeno were here, he would say that in order to put a penny into an empty box you would first have to put half the penny into the empty box, and it is no longer empty. And before you can put that half a penny in, you must first put in the bottom 1/2 of that 1/2 penny. So, it is impossible to put anything into an empty box.
If it’s Schrodinger’s box, it can be both empty and full of pennies.
If I understand the concept, it would be next to impossible to put anything in that box.
The box was never empty in the first place. It’s full of air.
The coins and the box are inside a vacuum.
I have heard this with a different answer. What I heard was the runner can only run into the forest for 1 mile, after that, he is running out of the forest.
I hate pseudospiritual claptrap like that. If you ask “What the hell does that mean?”, the responder will squint the eyes slightly, give a half-smile and a variation of “In time will come understanding.”
