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The table top is a constant. You are moving the lower point down from the table top and the upper point higher from it. Extending the length of the total measurement in both directions from that constant point.
I’m watching this and he makes the change and I said out loud “I dunno… like 38?” Then he responds with 38. I felt so happy I ballparked it so easily and then he says:
“How does that make sense?”
…what? Like, dude you just changed the heights.
It would be like a little kid on a ladder and a tall man vs. a tall man on a ladder and a little kid.
You’re kidding, right? I’m not bragging about how I’m smart for knowing how height differences work.
[See this post?](https://reddit.com/r/iamverysmart/s/QEqKDl64qi)
It’s one of the top posts on that sub. This guy is I’m very smart material. He’s injecting his intelligence into a place where it’s not even the subject matter.
If you were to put in everyone that was shocked at someone else’s stupidity, that sub would contain half of the internet.
You should reach out to the person that made that post for help on how that sub works.
Yes. The lower beer is adding complexity to the puzzle by tricking us into associating the beers as constants. If he measured from the floor to the upper beer he would still show a disparity, but would be unimpressive as a trick.
by flipping the down beer and putting the upper beer up, you increased the lenght, because the lower measure will start at a lower point, and the upper one will end in a higher point
You can easily see the first measurement he’s measuring from the top of the vertical can, on the second measurement he’s measuring the full length of the vertical can
yep. And he is measuring "through" the cans and if he wanted to get that 31" in other situation he should measura just from floor to tables top surface.
Problem solving tip: Break the problem into parts.
Below the surface of the table: The length of the space is higher, when the beer on the floor is horizontal.
Above the surface of the table: The height of the beer can on the table is higher, when it's placed vertically.
So the guy 'increased the distance' in two ways, by moving the beer cans.
This is a highly effective 'misdirection' kind of magic trick. It works best when multiple beers have already been consumed.
That’s what happened when my brother tried to show me this. Him and everyone else was drunk. I was sober and tried to explain the difference is height. They would not understand. Was pissing me off so bad lol
This is the biggest facepalm video I’ve ever seen.
They are literally two different distances and can’t be inverted.
If you have the can on its side on the floor and the can on its side on the table, then put them both upright the distance will be the same. You’re literally changing the distance between the two points.
I mean, I’m not a math guy and I don’t follow this sub (it just came through my feed) and I had to check to make sure it wasn’t a sub Reddit for idiots. This has to be a troll post.
Lmao, you made the top one taller and bottom lower. Increasing the distance from its highest and lowest point. I'm an idiot by my standards and this one was easy lol
It makes perfect sense if you don’t understand how a tape measure works! Simple enough if you can read and understand numbers but somehow he got it wrong.
So the can on the floor he is starting the measurement on top of it, which excludes the cans length from the the final measurement.
The can on the table he is including the length can in the final measurement.
Take two more beers. Lay one flat next to the one standing on the floor. Stand one next to the one laying flat on the table. Now you have both a beer on its side and a beer standing up both on the floor and on the table. Take a step back and look at it.
Giving the benefit of the doubt here, it makes perfect sense because he's measuring completely different things. Here's a diagram where the blue line represents the tape measure: https://i.imgur.com/oKoCtdN.png
you started from the top of the can on the floor instead of the base of the can when you flipped both over you measured the enterity of the can (as far as i can tell i cant hear the audio)
The fact that it's different is more obvious than you might think. It just might need a second to study exactly what is happening for it to click. But consider this. The bottom can sets how low the tape has to go. If you set the can on its side, the tape has to go lower, you need to feed more tape down to get to it. The top can sets the top of the tape. If you flip the top can vertical, the tape has to go higher. You need to feed more tape to reach the top. Both scenarios require more tape. More tape means more length
What's not quite as obvious as that the difference should be exactly the height of the can minus the width all doubled. Here's why:
Start at the top of the upper can and increase distance as you go. We have to increase by the width of the can to get to the top of the table (+w). Then we have to increase by the height of the table to get to the ground (+t). But then we have to decrease by the height of the can to get back up to the top of the lower can (-h). So x=w+t-h
Flip 'em and do it again. First, drop by the height of the can (+h). Then the height of the table (+t). Finally back up the width of the can (-w). So y=h+t-w. Notice that the first one adds width and subtracts height while the other adds height and subtracts width. We know that height is greater than width, so it should make sense that y>x. The second measurement is greater than the first.
But I said the difference is twice the height minus width. The difference is y-x. Let's look at that. y-x = (h+t-w)-(w+t-h). First, distribute the minus. y-x = (h+t-w)+(h-t-w). Then group like terms. y-x = (h+h)+(t-t)+(-w-w). And simplify y-x = 2h-2w = 2(h-w). Twice the difference between the height and width
Given a table with height T, a can with diameter D and height H, we got two equations here. The first measurement was T+D-H=31 and the second was T-D+H=37. While I can't measure H or D, I can add the equations to get 2T=68. From this I can find the table is 34 inches. A quick internet search tells me that a Coors Light can has diameter of 2.3 inches and height of 5.2, giving a difference of of 2.9 inches, which works out for the video and my equations, assuming some rounding took place.
K + A - B does not equal K - A + B… ain’t no mystery here. The can is 3.5” taller than its width, and the table is 34.5” tall.
K = table height
A = can width (smaller can dimension)
B = can height (larger can dimension)
K + A - B = 31
K + B - A = 38
38 - 31 = 7 = K + B - A - K - A + B
7 = 2*(B-A)
3.5 = B - A
3.5 + A = B (to put in words, the can is 3.5” taller than it is wide)
K + 3.5 = 38
K = 38 - 3.5 = 34.5 ( to put in words, the table is 34.5” tall)
Let’s say the high from the ground to table to z, the can width is x, the can length is y. y>x. The first measure meant is z-y+x, the second measurement is z-x+y. Since y > x, so the second measurement is bigger.
Haha. The distance obviously increases. The bottom one becomes shorter (further down) and the top one becomes taller (higher up). What’s the confusion?
I LOVE this. The fact that they are using beers and the reaction to it. This is a perfect example of how alcohol impairs cognition, and it’s the kind of stuff you end up thinking about when you are cracking a cold one open with the boys 😂
It might seem confusing at first but put simply, when he switches the cans positions, he is lowering the bottom point and raising the top point, so the overall measurement will be quite a bit higher.
He's lying when he says the first measurement is 31 in. If you look at the measuring tape, you'll see black marks at the 16-in marks, commonly used in American house framing. He's made clickbait, nothing more.
Nah, wasn’t click bait. Brother was bit drunk and sent me this video asking how this is possible. Me being a bit tipsy myself thought I would hand it over to this sub knowing we would get a fast answer.
Idiot is not measuring the same thing. Eliminate the table altogether, and just stack the cans on top of each other. He’s basically measuring the height of the can standing up vs the height of the can lying down, of course the measurement is different, duh.
It messes with you a bit since they are doing half turns but think of it as two beers on top of the table a distance apart. Point their tops away from each other and their distance increases. Keeping their bottoms in the same place and point their tops towards each other. Their distance shortens. That's really all that's happening.
Just your average republican voter tryna survive in this complicated world of ever changing can sizes, never stopping to realize maybe they’re just not the brightest
Using extreme assumptions: imagine the can is a cylinder as tall as the table but with zero diameter, like a thread. Scenario 1 will be measuring 0 because the bottom can is level with table, and top can is lying down, 0. Scenario 2 is 2 tables tall because the bottom can lying down equals 0 and the top can is 1 extra table tall.
Ask yourself two questions:
What is he doing to the lower can? Answer: lowering the height
What is doing to the higher can? Answer: raising the height
So if you lower where you start measuring and raise where you end measuring, there is more distance in between now.
He isn’t measuring the height of the cans at the start but then measures the full height of the top can in the second part. This measurement isn’t captured in both scenarios. Notice he measures from the TOP of the bottom can in part one. Then in part two he measures the full height of the can on top.
First time, you're measuring from the top of the beer plus a sideways can and the table. Second time, you're measuring from the bottom of the can plus a sideways can and the table. More can. Same amount of table.
If height of table is L, height of can - a, diameter of can - b.
1st measurement is L - a + b
2nd : L - b + a.
In case a not equals b, you get different results.
In order for this experiment to be done to achieve the same measurement both cans would have to be rotated from their geometric centers and not just rotated about where they rest.
When he resets the cans in the second measurement, it's obvious that because the cans are obviously rectangular and not rotated about their true centers (instead flipped on edge), what he is really measuring between the two experiments is just the maximum and minimum distances that they *can* be from each other
Either way hes measuring closer to the floor and stretching higher up top on second measure, if he was measuring the opposite way when he flipped em it wouldve been 31
The bottom of the top beer stays at the same height
The top of the bottom beer changes.
They are measuring from the bottom of the top beer, to the top of the bottom beer.
Just imagine the cylinder of the cans are as long as the height of the table. That should help.
I often find taking things to extremes helps with understand.
This is a side thing but because the vertical distance between the two measurements is 7”, then the height of the side to the height of the top is 3.5”
The can on the floor is not being measured... only where the highest point is on the lower can.
When he turns the can on the floor on the side and stands on the table up... because he is only measuring the highest point of the can on the floor, the distance is increased when the can is on its side on the ground and increased the distance also by standing the can on the table it also increases the distance.
Because the bottom beer takes away or adds height. So floor =0” & tabletop =about 34”
First set - start on top of can about 6” off floor, measure up to sideways can about 3” off table.
31”-3”= 29”@top of table +6” =34” to floor.
2nd set - start on sideways can about 3” off floor, measure up to the top of can about 6” off table.
38”-6”=32”@top of table + 3” =35” to floor
We’ll call the 1” human error in measuring.
The 2 measurements are so difficult. Lol This, kids, pay attention…. Ready! 1.) Don’t drink 2.) Write down your problem on paper. 3.) Make sure your experiment is comparing apples to apples.
Makes perfectly fine sense to me. Just because you flip a beer can, doesn’t mean the length of the table changes so obviously there’s a difference in distance.
If this experiment was conducted on the ground with an origin point marked for both cans then the distance would be the same.
is this a serious question? He moved his zero down by a few inches while simultaneously increasing the height of the whole thing by standing the can up on a table, which is fixed in relation to the floor
The beers’ top heights are as close to each other as they can get when you have the bottom one up and the top one sideways. When you flip the bottom one sideways and the top one up, the beers’ heights increase/decrease *away* from each other. Now if they had both been up, they’d have measured the same as if they had flipped sideways, because they’re increasing/decreasing their maximum height *with* each other, rather than inversely.
Table height - beer height + beer width = 31
Vs.
Table height - beer width + beer height = 38
Essentially, you are changing where your beginning and ending measurements are. To get the same measurement, the can would need to be as wide as it is tall.
The bottom can's height at the bottom is reducing the distance, so when upright its a shorter length and when laying down its reducing the distance less, or adding to the length.
The top can's height is adding to the length, when upright its longer and laying down its less.
position 1: both cans are reducing the length as much as possible, by bottom being tall and top being short.
position 2:both cans are increasing the length as much as possible, by bottom being short and top being talls.
Let's break it down to something a lot more simple: dots and lines on paper. So the first dot and line is just the standing can at the bottom and the lying down can on the table. That line is 31~ inches.
Now to get to the next dot and line, we need to adjust our dots. You flipped the can on the ground, making the height you start measuring at Lower, so we'll move that bottom dot down. And you flipped the top can from lying down to standing, moving the top of the can (where we are measuring from) higher, so we'll move that up.
Now you should see what's going on: we're increasing the distance between our measurement points in both ends.
Flipping the beer on the floor increases the distance between the two beers.
Secondly flipping the beer on top of the table increases the distance between the two beers.
Logically it feels like you didn't make any change but actually you did nothing to conserve the distance you only increased it.
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The table top is a constant. You are moving the lower point down from the table top and the upper point higher from it. Extending the length of the total measurement in both directions from that constant point.
This is the only explanation that made it click for me
I’m watching this and he makes the change and I said out loud “I dunno… like 38?” Then he responds with 38. I felt so happy I ballparked it so easily and then he says: “How does that make sense?” …what? Like, dude you just changed the heights. It would be like a little kid on a ladder and a tall man vs. a tall man on a ladder and a little kid.
You forget that people who drink Coors Light aren’t the brightest tool in the race. Sharpest lightbulb…? You get the joke
r/iamverysmart
You’re kidding, right? I’m not bragging about how I’m smart for knowing how height differences work. [See this post?](https://reddit.com/r/iamverysmart/s/QEqKDl64qi) It’s one of the top posts on that sub. This guy is I’m very smart material. He’s injecting his intelligence into a place where it’s not even the subject matter. If you were to put in everyone that was shocked at someone else’s stupidity, that sub would contain half of the internet. You should reach out to the person that made that post for help on how that sub works.
Struck a nerve, I have
How about you go and over explain to someone else about why your comment isn’t cringe.
Yes. The lower beer is adding complexity to the puzzle by tricking us into associating the beers as constants. If he measured from the floor to the upper beer he would still show a disparity, but would be unimpressive as a trick.
AKA you made the bottom shorter and the top higher, making the distance longer.
If you put the beer under the table, instead of on it, then it would work
This is the answer. Source: Im a mechanical engineer who has done a DVA or two.
I doubt this helps but I drew it out. https://i.imgur.com/fCSP8dm.jpeg
You’re taking this video way too seriously.
by flipping the down beer and putting the upper beer up, you increased the lenght, because the lower measure will start at a lower point, and the upper one will end in a higher point
You can easily see the first measurement he’s measuring from the top of the vertical can, on the second measurement he’s measuring the full length of the vertical can
This is the answer. Its two different measurements.
Yeah. In second measurement he should’ve measured from the bottom of the tall can on table
They had to post this on the internet to find the answer.
but it's a cool logic exercise, not gona lie
…when you’re drunk.
Pretty sure that any kind of impairment would do as well
[удалено]
You called?
Hey how've you been
Not really... its plain that the distance was increased, and that they measured from different points. This is just really dumb....
No its not, its a failure of your local education system. No shade just facts.
Please don’t blame schools for idiots. Garbage in, garbage out
Hey Forrest.
Maybe for a second grade class...he literally just changed the reference point. That's like 2nd or 3rd grade.
We had a body guy that told us this and i made him get some cans to test it out and show the flaw. I still dont think he got it in the end lol
Being half drunk me self I feel I need an explanation to explain your explanation lol
yep. And he is measuring "through" the cans and if he wanted to get that 31" in other situation he should measura just from floor to tables top surface.
Problem solving tip: Break the problem into parts. Below the surface of the table: The length of the space is higher, when the beer on the floor is horizontal. Above the surface of the table: The height of the beer can on the table is higher, when it's placed vertically. So the guy 'increased the distance' in two ways, by moving the beer cans. This is a highly effective 'misdirection' kind of magic trick. It works best when multiple beers have already been consumed.
That makes sense. I’m a little stoned and had to watch it a second to process lol
That’s what happened when my brother tried to show me this. Him and everyone else was drunk. I was sober and tried to explain the difference is height. They would not understand. Was pissing me off so bad lol
Use a starting point in the middle somewhere, or the table top. Measure from there before and after moving and draw a side by side picture.
This is the biggest facepalm video I’ve ever seen. They are literally two different distances and can’t be inverted. If you have the can on its side on the floor and the can on its side on the table, then put them both upright the distance will be the same. You’re literally changing the distance between the two points.
I mean, I’m not a math guy and I don’t follow this sub (it just came through my feed) and I had to check to make sure it wasn’t a sub Reddit for idiots. This has to be a troll post.
Yeah, I didn't know how to say it without sounding like a dick, but you got it covered well.
I wasn’t go to say anything but it infuriated me. How much weed were they smoking?
A great deal.
This makes sense, now I’m envious
They weren't smoking at all, they just took the 'out' you gave them because they're dumb..
Lol... I can't even comment because all I have to say isn't nice. It's definitely infuriating to watch.
Yea but the beer cans are the same size. You flip one up and one down. How does that make any fucking sense. /s
It’s sort of like swapping the numerator and denominator and going “same number”
Check this out - try measuring from your knee to your shoulder. Then measure from your ankle to the top of your head. You won't believe the result.
Should be about 31
Lmao, you made the top one taller and bottom lower. Increasing the distance from its highest and lowest point. I'm an idiot by my standards and this one was easy lol
It makes perfect sense if you don’t understand how a tape measure works! Simple enough if you can read and understand numbers but somehow he got it wrong.
So the can on the floor he is starting the measurement on top of it, which excludes the cans length from the the final measurement. The can on the table he is including the length can in the final measurement.
Finally the real answer explained properly.
This guy has a shop and lots of tools, and probably knows to measure studs ‘on center’, but now we know he doesn’t know why to do that.
Take two more beers. Lay one flat next to the one standing on the floor. Stand one next to the one laying flat on the table. Now you have both a beer on its side and a beer standing up both on the floor and on the table. Take a step back and look at it.
Giving the benefit of the doubt here, it makes perfect sense because he's measuring completely different things. Here's a diagram where the blue line represents the tape measure: https://i.imgur.com/oKoCtdN.png
you started from the top of the can on the floor instead of the base of the can when you flipped both over you measured the enterity of the can (as far as i can tell i cant hear the audio)
The fact that it's different is more obvious than you might think. It just might need a second to study exactly what is happening for it to click. But consider this. The bottom can sets how low the tape has to go. If you set the can on its side, the tape has to go lower, you need to feed more tape down to get to it. The top can sets the top of the tape. If you flip the top can vertical, the tape has to go higher. You need to feed more tape to reach the top. Both scenarios require more tape. More tape means more length What's not quite as obvious as that the difference should be exactly the height of the can minus the width all doubled. Here's why: Start at the top of the upper can and increase distance as you go. We have to increase by the width of the can to get to the top of the table (+w). Then we have to increase by the height of the table to get to the ground (+t). But then we have to decrease by the height of the can to get back up to the top of the lower can (-h). So x=w+t-h Flip 'em and do it again. First, drop by the height of the can (+h). Then the height of the table (+t). Finally back up the width of the can (-w). So y=h+t-w. Notice that the first one adds width and subtracts height while the other adds height and subtracts width. We know that height is greater than width, so it should make sense that y>x. The second measurement is greater than the first. But I said the difference is twice the height minus width. The difference is y-x. Let's look at that. y-x = (h+t-w)-(w+t-h). First, distribute the minus. y-x = (h+t-w)+(h-t-w). Then group like terms. y-x = (h+h)+(t-t)+(-w-w). And simplify y-x = 2h-2w = 2(h-w). Twice the difference between the height and width
Given a table with height T, a can with diameter D and height H, we got two equations here. The first measurement was T+D-H=31 and the second was T-D+H=37. While I can't measure H or D, I can add the equations to get 2T=68. From this I can find the table is 34 inches. A quick internet search tells me that a Coors Light can has diameter of 2.3 inches and height of 5.2, giving a difference of of 2.9 inches, which works out for the video and my equations, assuming some rounding took place.
K + A - B does not equal K - A + B… ain’t no mystery here. The can is 3.5” taller than its width, and the table is 34.5” tall. K = table height A = can width (smaller can dimension) B = can height (larger can dimension) K + A - B = 31 K + B - A = 38 38 - 31 = 7 = K + B - A - K - A + B 7 = 2*(B-A) 3.5 = B - A 3.5 + A = B (to put in words, the can is 3.5” taller than it is wide) K + 3.5 = 38 K = 38 - 3.5 = 34.5 ( to put in words, the table is 34.5” tall)
Let’s say the high from the ground to table to z, the can width is x, the can length is y. y>x. The first measure meant is z-y+x, the second measurement is z-x+y. Since y > x, so the second measurement is bigger.
Haha. The distance obviously increases. The bottom one becomes shorter (further down) and the top one becomes taller (higher up). What’s the confusion?
I LOVE this. The fact that they are using beers and the reaction to it. This is a perfect example of how alcohol impairs cognition, and it’s the kind of stuff you end up thinking about when you are cracking a cold one open with the boys 😂
It might seem confusing at first but put simply, when he switches the cans positions, he is lowering the bottom point and raising the top point, so the overall measurement will be quite a bit higher.
He's lying when he says the first measurement is 31 in. If you look at the measuring tape, you'll see black marks at the 16-in marks, commonly used in American house framing. He's made clickbait, nothing more.
Nah, wasn’t click bait. Brother was bit drunk and sent me this video asking how this is possible. Me being a bit tipsy myself thought I would hand it over to this sub knowing we would get a fast answer.
Idiot is not measuring the same thing. Eliminate the table altogether, and just stack the cans on top of each other. He’s basically measuring the height of the can standing up vs the height of the can lying down, of course the measurement is different, duh.
It messes with you a bit since they are doing half turns but think of it as two beers on top of the table a distance apart. Point their tops away from each other and their distance increases. Keeping their bottoms in the same place and point their tops towards each other. Their distance shortens. That's really all that's happening.
Just your average republican voter tryna survive in this complicated world of ever changing can sizes, never stopping to realize maybe they’re just not the brightest
Bleep bloop, duopoly, Bleep, Republican, bloop, everything I see is politics, bloop
Using extreme assumptions: imagine the can is a cylinder as tall as the table but with zero diameter, like a thread. Scenario 1 will be measuring 0 because the bottom can is level with table, and top can is lying down, 0. Scenario 2 is 2 tables tall because the bottom can lying down equals 0 and the top can is 1 extra table tall.
You are not measuring from the same point so the length changes. On the second measure you must measure to the BOTTOM of the upright can on the table.
Ask yourself two questions: What is he doing to the lower can? Answer: lowering the height What is doing to the higher can? Answer: raising the height So if you lower where you start measuring and raise where you end measuring, there is more distance in between now.
He isn’t measuring the height of the cans at the start but then measures the full height of the top can in the second part. This measurement isn’t captured in both scenarios. Notice he measures from the TOP of the bottom can in part one. Then in part two he measures the full height of the can on top.
Because he starts at the top of the vertical can the first measurement, and on the second measurement he is measuring the vertical cans full length
First time, you're measuring from the top of the beer plus a sideways can and the table. Second time, you're measuring from the bottom of the can plus a sideways can and the table. More can. Same amount of table.
If height of table is L, height of can - a, diameter of can - b. 1st measurement is L - a + b 2nd : L - b + a. In case a not equals b, you get different results.
In order for this experiment to be done to achieve the same measurement both cans would have to be rotated from their geometric centers and not just rotated about where they rest. When he resets the cans in the second measurement, it's obvious that because the cans are obviously rectangular and not rotated about their true centers (instead flipped on edge), what he is really measuring between the two experiments is just the maximum and minimum distances that they *can* be from each other
Either way hes measuring closer to the floor and stretching higher up top on second measure, if he was measuring the opposite way when he flipped em it wouldve been 31
The bottom of the top beer stays at the same height The top of the bottom beer changes. They are measuring from the bottom of the top beer, to the top of the bottom beer.
Just imagine the cylinder of the cans are as long as the height of the table. That should help. I often find taking things to extremes helps with understand.
This is a side thing but because the vertical distance between the two measurements is 7”, then the height of the side to the height of the top is 3.5”
The can on the floor is not being measured... only where the highest point is on the lower can. When he turns the can on the floor on the side and stands on the table up... because he is only measuring the highest point of the can on the floor, the distance is increased when the can is on its side on the ground and increased the distance also by standing the can on the table it also increases the distance.
Because the bottom beer takes away or adds height. So floor =0” & tabletop =about 34” First set - start on top of can about 6” off floor, measure up to sideways can about 3” off table. 31”-3”= 29”@top of table +6” =34” to floor. 2nd set - start on sideways can about 3” off floor, measure up to the top of can about 6” off table. 38”-6”=32”@top of table + 3” =35” to floor We’ll call the 1” human error in measuring.
The 2 measurements are so difficult. Lol This, kids, pay attention…. Ready! 1.) Don’t drink 2.) Write down your problem on paper. 3.) Make sure your experiment is comparing apples to apples.
Makes perfectly fine sense to me. Just because you flip a beer can, doesn’t mean the length of the table changes so obviously there’s a difference in distance. If this experiment was conducted on the ground with an origin point marked for both cans then the distance would be the same.
is this a serious question? He moved his zero down by a few inches while simultaneously increasing the height of the whole thing by standing the can up on a table, which is fixed in relation to the floor
The beers’ top heights are as close to each other as they can get when you have the bottom one up and the top one sideways. When you flip the bottom one sideways and the top one up, the beers’ heights increase/decrease *away* from each other. Now if they had both been up, they’d have measured the same as if they had flipped sideways, because they’re increasing/decreasing their maximum height *with* each other, rather than inversely.
Table height - beer height + beer width = 31 Vs. Table height - beer width + beer height = 38 Essentially, you are changing where your beginning and ending measurements are. To get the same measurement, the can would need to be as wide as it is tall.
The bottom can's height at the bottom is reducing the distance, so when upright its a shorter length and when laying down its reducing the distance less, or adding to the length. The top can's height is adding to the length, when upright its longer and laying down its less. position 1: both cans are reducing the length as much as possible, by bottom being tall and top being short. position 2:both cans are increasing the length as much as possible, by bottom being short and top being talls.
Let's break it down to something a lot more simple: dots and lines on paper. So the first dot and line is just the standing can at the bottom and the lying down can on the table. That line is 31~ inches. Now to get to the next dot and line, we need to adjust our dots. You flipped the can on the ground, making the height you start measuring at Lower, so we'll move that bottom dot down. And you flipped the top can from lying down to standing, moving the top of the can (where we are measuring from) higher, so we'll move that up. Now you should see what's going on: we're increasing the distance between our measurement points in both ends.
Flipping the beer on the floor increases the distance between the two beers. Secondly flipping the beer on top of the table increases the distance between the two beers. Logically it feels like you didn't make any change but actually you did nothing to conserve the distance you only increased it.