# Beer cans on the floor and table.

#### Tonyr1084

Joined Sep 24, 2015
7,555
I don't know if this is "Cool" "Amazing" or "A Joke". Can anyone explain it to me?

MOD EDIT: This was copied from a post in The Jokes Thread to contain the side discussion that resulted.

Last edited by a moderator:
• djsfantasi

#### MrSalts

Joined Apr 2, 2020
2,767
I don't know if this is "Cool" "Amazing" or "A Joke". Can anyone explain it to me?
Have you tried it? When you measure by the second method, make sure your camera zooms in so nobody can see that you put the end of the tape measure on the ground, not on the can. It works every time.

#### ElectricSpidey

Joined Dec 2, 2017
2,635

Above and below a reference point.

#### ThePanMan

Joined Mar 13, 2020
707
The explanation is rather simple. The cans are 4 3/4" tall and 2 1/2" wide (diameter).

When the can on the floor is upright it sets the distance from the top of the can to the top of the table at 25 3/4" high. So the table top is 30 1/2" from the floor. Forget that for a moment. It's actually irrelevant because we're not measuring from the floor but from 4 3/4" above the floor. Ad in the diameter of the can to the 25 3/4" and you get 28 1/4" (as is apparent in the video).

Now let's change things up: Lay the floor can on its side. The distance from the side of the standing can to the table top is 27 3/4". Now add in the height of the can standing up on the table top. You've gotten 32 1/4". The difference from 32 1/4" and 28 1/4" is 4 inches. Keep in mind the measurements shown in the video are not exactly the numbers I've chosen but mine are close. I'm only off by 1/4"

So by flipping the cans you are effectively measuring the height of only one can.

Another contributing factor to the inaccuracy of the numbers is the the guy measures from the can LID on the floor, which isn't the same height as the rim of the can on the table when it's standing upright.
[end edit]

#### ElectricSpidey

Joined Dec 2, 2017
2,635
Nice explanation...here's a shorter one.

Using the table top as the reference point...

Both the distances above and below the reference points are shorter in the first measurement than in the second.

#### djsfantasi

Joined Apr 11, 2010
9,131
Nice explanation...here's a shorter one.

Using the table top as the reference point...

Both the distances above and below the reference points are shorter in the first measurement than in the second.

#### WBahn

Joined Mar 31, 2012
29,511
I don't know if this is "Cool" "Amazing" or "A Joke". Can anyone explain it to me?
Not cool or amazing, and no trick necessary -- making the claim that the two measurements should be the same creates the expectation that rotating both cans should have no effect on the measurement, which at first blush seems reasonable.

So then when they aren't, many people immediately start looking for some trickery in how the video was made. Instead, ask whether or not the claim itself holds up. To see whether or not it does, just do the math.

You have two identical rectangular objects, WxL (L>W)

You have a table that is height H above the floor.

First measurement: Set one object upright on the floor and the second on it's side on the table.

H1 = height of top of floor object = L
H2 = height of top of table object = H + W

Distance from top of floor object to top of table object:

D1 = H2 - H1 = (H+W) - L = H - (L-W)

Second measurement: Set one object on it's side on the floor and the second upright on the table.

H3 = height of top of floor object = W
H4 = height of top of table object = H + L

Distance from top of floor object to top of table object:

D2 = H4 - H3 = (H+L) - W = H + (L-W)

So the second measurement is greater than the first measurement by

D2 - D1 = [H + (L-W)] - [H - (L-W)] = 2(L-W)

So all he determined is that a beer can is about two inches taller than it is wide.

#### WBahn

Joined Mar 31, 2012
29,511
The explanation is rather simple. The cans are 4 3/4" tall and 2 1/2" wide (diameter).

When the can on the floor is upright it sets the distance from the top of the can to the top of the table at 25 3/4" high. So the table top is 30 1/2" from the floor. Forget that for a moment. It's actually irrelevant because we're not measuring from the floor but from 4 3/4" above the floor. Ad in the diameter of the can to the 25 3/4" and you get 28 1/4" (as is apparent in the video).

Now let's change things up: Lay the floor can on its side. The distance from the side of the standing can to the table top is 27 3/4". Now add in the height of the can standing up on the table top. You've gotten 32 1/4". The difference from 32 1/4" and 28 1/4" is 4 inches. Keep in mind the measurements shown in the video are not exactly the numbers I've chosen but mine are close. I'm only off by 1/4"

So by flipping the cans you are effectively measuring the height of only one can.
Nope. That's not what you are measuring. If that were the case, then what would you expect to happen if the cans were cubes? Now, by symmetry, the measurements have to the same, not different by an amount determined by the height of one of the cans.

What you are effectively measuring is how much taller the can is than it is wide.

#### ThePanMan

Joined Mar 13, 2020
707
what would you expect to happen if the cans were cubes?
Cubes? As in all six sides having the same dimension? I don't understand your comment.

#### WBahn

Joined Mar 31, 2012
29,511
Cubes? As in all six sides having the same dimension? I don't understand your comment.
Cubes was a simple way of expressing the notion that the height and width of the cans are the same.

Your analysis was that the two measurements in the video amounted to measuring the height of a can. They don't -- although that's in the ballpark. If the cans were as wide as they are high, then rotating them 90° would have no impact on the measurements. The difference is due to solely to the difference between the width and height of a can.

With cans that are small compared to the height of the table, and also where the difference between the height and the width is relatively small compared to the total distance measured, the effect is hard to grasp intuitively, The "trick" relies on this. But imagine using something like a 2"x4" that was just a few inches shorter than the height of the table. Now the fact that the two measurements are measuring drastically different things is so obvious that I doubt anyone could miss it.

#### ThePanMan

Joined Mar 13, 2020
707
If the cans were as wide as they are high, then rotating them 90° would have no impact on the measurements.
Never said the cans were the same height regardless of orientation. Here's what I mean: (a picture paints a thousand words)
The difference between the totals of A versus B show how with one set of orientations the measurement would be (approximately) 28 1/4" versus 32 3/4". This is why the video shows a difference in height. One would presume that since the person presenting the video said to expect the same results one would fall into that expectation. Only took me a few seconds to realize what was going on. No need for algebraic expressions. The solution is simple if you use the table top
Using the table top as the reference point...
as the point of reference and measure both up and down then add the two measurements together to come to a conclusion. This is just like the puzzle of why three men paid $30 for a room costing only$25. The clerk realized the mistake and repaid the three men a dollar each and he kept two dollars for himself. Hence, the three men paid $9 each for a total of$27 and the clerk kept $2 (which adds up to$29). Where did the other dollar go? Nowhere. In reality each man paid $9, totaling$27. The clerk kept $2. The difference isn't in what they initially paid, it's in the cost of the room ($25). They overpaid by two dollars, the same two the clerk kept for himself.

The moral of each story is "Don't be lead into thinking something, come to your own conclusion." • shortbus

#### SamR

Joined Mar 19, 2019
4,913
@ThePanMan which CAD app did you use for that? I need a nice simple one...

#### WBahn

Joined Mar 31, 2012
29,511
Never said the cans were the same height regardless of orientation. Here's what I mean: (a picture paints a thousand words)
The difference between the totals of A versus B show how with one set of orientations the measurement would be (approximately) 28 1/4" versus 32 3/4". This is why the video shows a difference in height. One would presume that since the person presenting the video said to expect the same results one would fall into that expectation. Only took me a few seconds to realize what was going on. No need for algebraic expressions. The solution is simple if you use the table top
Except that your conclusion was not correct.

Your conclusion was, "So by flipping the cans you are effectively measuring the height of only one can."

This is simply not true. Do the math.

The case of the cans being the same height regardless of orientation is the counter-example that proves that your conclusion is not correct. In that case, symmetry demands that the two measurements be identical, regardless of what the height of the can is, hence you cannot be effectively measuring the height of only one can.

The difference in the two measurements (in your illustration) is 4.5".

If your conclusion is correct and your are effectively measuring the height only one can, how do you get from 4.5" to the can height, which is 4.75"?

If, instead, you actually do the math you discover that the difference in the two measurements is NOT related to the height of the can, but rather to the difference between the height and the width of the cans. Specifically, the difference in the measurements is twice the difference between height and width. Which means that, based on the difference of 4.5" in your illustration, each can is 2.25" taller than it is wide. Sure enough, your cans are 4.75" tall and 2.5" wide, for a difference of 2.25".

That same difference in measurement would have resulted if each can had been 10" wide and 12.25" tall, or 30" wide and 32.25" tall.

#### MrSalts

Joined Apr 2, 2020
2,767
Except that your conclusion was not correct.

Your conclusion was, "So by flipping the cans you are effectively measuring the height of only one can."

This is simply not true. Do the math.

The case of the cans being the same height regardless of orientation is the counter-example that proves that your conclusion is not correct. In that case, symmetry demands that the two measurements be identical, regardless of what the height of the can is, hence you cannot be effectively measuring the height of only one can.

The difference in the two measurements (in your illustration) is 4.5".

If your conclusion is correct and your are effectively measuring the height only one can, how do you get from 4.5" to the can height, which is 4.75"?

If, instead, you actually do the math you discover that the difference in the two measurements is NOT related to the height of the can, but rather to the difference between the height and the width of the cans. Specifically, the difference in the measurements is twice the difference between height and width. Which means that, based on the difference of 4.5" in your illustration, each can is 2.25" taller than it is wide. Sure enough, your cans are 4.75" tall and 2.5" wide, for a difference of 2.25".

That same difference in measurement would have resulted if each can had been 10" wide and 12.25" tall, or 30" wide and 32.25" tall.
You are just using a different frame of reference than @ThePanMan - you're both saying the same thing.

#### ThePanMan

Joined Mar 13, 2020
707

#### ThePanMan

Joined Mar 13, 2020
707
Do the math.
I guess you don't read pictures.
how do you get from 4.5" to the can height, which is 4.75"?
The can diameter is 2 1/2", not 2 1/4".

Far as I'm concerned, it's been explained. And @ElectricSpidey said it first - measure from the table top.

#### ThePanMan

Joined Mar 13, 2020
707
It's Super Bowl 57 Kickoff. I'm outa here.

#### WBahn

Joined Mar 31, 2012
29,511
You are just using a different frame of reference than @ThePanMan - you're both saying the same thing.
No, we are NOT saying the same thing. PanMan said that the measurement was effectively measuring the height of one can.

Please show how that measurement is effectively measuring the height of one can.

#### MrSalts

Joined Apr 2, 2020
2,767
No, we are NOT saying the same thing. PanMan said that the measurement was effectively measuring the height of one can.

Please show how that measurement is effectively measuring the height of one can.
Ha, then you'll come up with one more excuse to argue.

#### WBahn

Joined Mar 31, 2012
29,511
I guess you don't read pictures.
The can diameter is 2 1/2", not 2 1/4".

Far as I'm concerned, it's been explained. And @ElectricSpidey said it first - measure from the table top.
Yes, the can diameter is 2 1/2". The can height is 4 3/4".

What is the DIFFERENCE between the height of the can and the diameter of the can?

Hint, you SUBTRACT the diameter of the can (2 1/2") from the height of the can (4 3/4").

What do you get? You get 2 1/4".

Now double that. What do you get? You get 4 1/2".

What is the DIFFERENCE between the two measurements in your picture?

32.75" - 28.25" = 4.5"

That is NOT the height of one can, it is twice the amount by which each can is taller than it is wide.

You CANNOT take those two measurements and determine the height of a can.

If you still want to insist that you can, then show how.

Example #1.

I have a work table in my lab and I have two identical cans. I made the measurements the same way as in the video (and as in your diagram). The first measurement is 31". The second is 55".

How tall are the cans?

Example #2.

I have a different table in my office and I have two other identical cans. The first measurement is 29". The second is 29".

How tall are the cans?

If the measurements are effectively measuring the height of one can, then both of these questions should be easily answerable.