Delta Airlines magazine brain teaser error?
September 27th, 2013 at 10:13:03 PM
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As mentioned in other threads, my wife and I are currently on a trip to Lake Tahoe and San Diego. We are flying with Delta Airlines.
The Delta in-flight magazine has a puzzles page called "Who's Game?" The September issue has three brain teasers, for one of which I am confident they have provided the wrong answer in their bottom-of-the-page solutions. That is, unless I misunderstood the question or screwed up somewhere. I thought I would post the brain teaser here to see whether others agree that Delta's answer is incorrect (or even just for your entertainment.)
Other than the erroneous answer given, I thought it was a pretty good puzzle.
I suggest that puzzle solvers here post their answers only and be prepared to post detailed solutions later (behind spoiler buttons, I suppose) after we see whether there is concensus or dispute as to the answer. I have my answer and solution ready but not typed up. Work up your answer first, then take a look at:
The Delta in-flight magazine has a puzzles page called "Who's Game?" The September issue has three brain teasers, for one of which I am confident they have provided the wrong answer in their bottom-of-the-page solutions. That is, unless I misunderstood the question or screwed up somewhere. I thought I would post the brain teaser here to see whether others agree that Delta's answer is incorrect (or even just for your entertainment.)
Quote: Delta's "Who's Game?"Refrigerators come in cartons 40 inches deep by 48 inches wide by 60 inches high. They must stand upright when stored. If Jones has a storage room 45 feet across, 60 feet deep, and eight feet high, what is the greatest number of refrigerators he can store there?
A). 180
B). 195
C). 198
D). 201
E). 396
Other than the erroneous answer given, I thought it was a pretty good puzzle.
I suggest that puzzle solvers here post their answers only and be prepared to post detailed solutions later (behind spoiler buttons, I suppose) after we see whether there is concensus or dispute as to the answer. I have my answer and solution ready but not typed up. Work up your answer first, then take a look at:
A
September 27th, 2013 at 10:48:16 PM
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Doc, I also came up with a different answer.
Since the cartons have to be upright it limits the solution to two dimensions since the height of two or more cartons exceeds the height of the storage room. So then there are really only two options
1. Arrange the cartons with 48" edge across the 45' width of the storage room and align the 40" edge along the 60' depth. If you do this, it produces a 11x18 carton configuration with a total of 198 cartons
2. Arrange the cartons with 40" edge across the 45' width of the storage room and align the 48" edge along the 60' depth. If you do this, it produces a 13x15 carton configuration with a total of 195 cartons
Thus my answer is C, 198 cartons.
1. Arrange the cartons with 48" edge across the 45' width of the storage room and align the 40" edge along the 60' depth. If you do this, it produces a 11x18 carton configuration with a total of 198 cartons
2. Arrange the cartons with 40" edge across the 45' width of the storage room and align the 48" edge along the 60' depth. If you do this, it produces a 13x15 carton configuration with a total of 195 cartons
Thus my answer is C, 198 cartons.
September 28th, 2013 at 2:00:23 AM
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I came up with the same answer as MidwestAP. I assume you did too.
For the record, I also calculated the same incorrect answer that he provided, which was one of the choices, as well as five more incorrect answers that the true geometry challenged person can come up with. None of them are the same as Delta's other choices.
Since Delta provided the correct answer as well as the most common incorrect answer, I suspect the error lies in the magazine layout designer and not their math person.
I came up with 198. Of course, this assumes you can load all the way up to the doorway.
The most common incorrect answer is 195. This is the max it they are rotated 90 degrees.
If you screw up the math, options include 165, 234, 143 and 270.
If you merely consider the space and area of the carton, you'll come up with 202.5. Hopefully, when you get that fraction, you'll realize your mistake.
And you'll get even higher numbers if you ignore the part about storing them upright, and calculate for raw volume.
For the record, I also calculated the same incorrect answer that he provided, which was one of the choices, as well as five more incorrect answers that the true geometry challenged person can come up with. None of them are the same as Delta's other choices.
Since Delta provided the correct answer as well as the most common incorrect answer, I suspect the error lies in the magazine layout designer and not their math person.
I came up with 198. Of course, this assumes you can load all the way up to the doorway.
The most common incorrect answer is 195. This is the max it they are rotated 90 degrees.
If you screw up the math, options include 165, 234, 143 and 270.
If you merely consider the space and area of the carton, you'll come up with 202.5. Hopefully, when you get that fraction, you'll realize your mistake.
And you'll get even higher numbers if you ignore the part about storing them upright, and calculate for raw volume.
I invented a few casino games. Info:
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September 28th, 2013 at 4:37:28 AM
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Quote: MidwestAPDoc, I also came up with a different answer.
Since the cartons have to be upright it limits the solution to two dimensions since the height of two or more cartons exceeds the height of the storage room. So then there are really only two options
1. Arrange the cartons with 48" edge across the 45' width of the storage room and align the 40" edge along the 60' depth. If you do this, it produces a 11x18 carton configuration with a total of 198 cartons
2. Arrange the cartons with 40" edge across the 45' width of the storage room and align the 48" edge along the 60' depth. If you do this, it produces a 13x15 carton configuration with a total of 195 cartons
Thus my answer is C, 198 cartons.
Same result.
September 28th, 2013 at 7:27:54 AM
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I'm guessing I got Delta's answer.
201
The problem is that everyone assumes that all of the boxes are oriented in the same way. Regardless of how you fit them, the 60 foot wall will be filled completely, so now we need to orient boxes so that we can maximize the space along the 45 foot wall.
So, along the 45 foot wall (540 inches), you can make any pattern of boxes you want. The ones that have been considered are placing all 40 inch edges along the wall and placing all 48 inch edges against the wall:
If you place the 40 inch edges against this wall, you will have 20 inches of waste (13*40 = 520). (195 answer)
If you place the 48 inch edges, you will have 12 inches of waste (11*48 = 528). (198 answer)
Now, what if you place 11 40" edges and 2 48" edges against the 45' wall?
Alternatively, you could place 5 40" edges and 7 48" edges. In this case, you use 5*50+7*48 = 536 inches, and you only waste 4 inches.
201
The problem is that everyone assumes that all of the boxes are oriented in the same way. Regardless of how you fit them, the 60 foot wall will be filled completely, so now we need to orient boxes so that we can maximize the space along the 45 foot wall.
So, along the 45 foot wall (540 inches), you can make any pattern of boxes you want. The ones that have been considered are placing all 40 inch edges along the wall and placing all 48 inch edges against the wall:
If you place the 40 inch edges against this wall, you will have 20 inches of waste (13*40 = 520). (195 answer)
If you place the 48 inch edges, you will have 12 inches of waste (11*48 = 528). (198 answer)
Now, what if you place 11 40" edges and 2 48" edges against the 45' wall?
Alternatively, you could place 5 40" edges and 7 48" edges. In this case, you use 5*50+7*48 = 536 inches, and you only waste 4 inches.
I heart Crystal Math.
September 28th, 2013 at 10:14:04 AM
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Quote: CrystalMathI'm guessing I got Delta's answer.
I got the same final answer as CrystalMath (and the intermediates along the way.) I just think someone at the Delta mag screwed up.
But the fact that several members here found just the smaller answers shows what a good problem it is.
September 28th, 2013 at 10:47:50 AM
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I came up with this answer independently.Quote: MidwestAPDoc, I also came up with a different answer.
Since the cartons have to be upright it limits the solution to two dimensions since the height of two or more cartons exceeds the height of the storage room. So then there are really only two options
1. Arrange the cartons with 48" edge across the 45' width of the storage room and align the 40" edge along the 60' depth. If you do this, it produces a 11x18 carton configuration with a total of 198 cartons
2. Arrange the cartons with 40" edge across the 45' width of the storage room and align the 48" edge along the 60' depth. If you do this, it produces a 13x15 carton configuration with a total of 195 cartons
Thus my answer is C, 198 cartons.
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
September 28th, 2013 at 11:14:47 AM
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I got
woohoo! And the extra spoilers didn't help me figure out how delta screwed up...lol I think that's an obvious incorrect answer.
D. Generally you want to put the 4' width along with the 45' room length because you can pack 18 fridges perfectly per four feet. Doing this all the way until 44' of the room length is used is 11x18 = 198, C. If you flip the other way and pack them the other way, then you get 13 x 15 = 195, B. So putting the 4' fridge length along the 45' dimension is preferred. But we can do even better than that if we rotate the fridges. If we align 7 fridges by the 4' width then we can align 5 fridges with the remaining 17' of space. So this leads to: 7 x 18 + 5 x 15 = 201, D. I really don't get how they got A. I guess I will need to read the rest of the spoilers.
Quote: DocI got the same final answer as CrystalMath (and the intermediates along the way.) I just think someone at the Delta mag screwed up.
But the fact that several members here found just the smaller answers shows what a good problem it is.
woohoo! And the extra spoilers didn't help me figure out how delta screwed up...lol I think that's an obvious incorrect answer.
September 28th, 2013 at 11:55:52 AM
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I get 201 too.
Against the 720" warehouse wall place 15 boxes the long way. This will fit exactly: 15*48"=720".
Do this for 11 columns. This will consume 11*40" = 440" along the 540" wall, leaving 100" left. Total boxes so far = 15*11=165.
Against the other 720" warehouse wall place 18 boxes the short way. Do this for two columns, which will use 96" along the 540" wall. Additional boxes = 18*2=36.
165+36=201.
We still have a 720"x4" area left. However, there doesn't seem to be any way to completely cover the 540" wall, so we can't help but waste some space.
Against the 720" warehouse wall place 15 boxes the long way. This will fit exactly: 15*48"=720".
Do this for 11 columns. This will consume 11*40" = 440" along the 540" wall, leaving 100" left. Total boxes so far = 15*11=165.
Against the other 720" warehouse wall place 18 boxes the short way. Do this for two columns, which will use 96" along the 540" wall. Additional boxes = 18*2=36.
165+36=201.
We still have a 720"x4" area left. However, there doesn't seem to be any way to completely cover the 540" wall, so we can't help but waste some space.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 28th, 2013 at 3:29:13 PM
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Right now I am a little too lazy to check my work -- is answer E) the maximum possible if you ignore the restriction that the refrigerators must be stored upright? My initial calculation is that you could only fit 324 in the space that way, but maybe I'm wrong.
September 28th, 2013 at 5:41:59 PM
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I came up with 201 using 7 at 48" + 5 at 40" along the 540" wall. This provides 18 deep + 15 deep. The math solves as 18*7 + 15*5 = 201 refridgerators. I also have a 4" space along the 720" wall. So my answer is "D". I did not check spoilers.
I thought the answer was 198 given all boxes faced the same direction, which IS true, but its not the maximum given pattern packing. hint, hint.
Some people need to reimagine their thinking.
September 28th, 2013 at 8:07:06 PM
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Quote: DocRight now I am a little too lazy to check my work -- is answer E) the maximum possible if you ignore the restriction that the refrigerators must be stored upright? My initial calculation is that you could only fit 324 in the space that way, but maybe I'm wrong.
324 is the max possible if you can magically divide the fridges to fill all the available space. I dunno where they got E).
September 28th, 2013 at 8:24:38 PM
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I think you may be confusing the definition of "Greatest". 180 is a really great number. All of the other numbers are inferior!Quote: DocA
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
September 28th, 2013 at 11:45:01 PM
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180 makes me think Delta put an aisle in the room to access all the fridges. Kinda fits airline thinking, ehh.
Some people need to reimagine their thinking.
September 29th, 2013 at 3:11:49 AM
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The same refrigerator packing puzzle appears on http://werbil.com/uploads/World%E2%80%99s_200_Hardest_Brain_Teasers.pdf
They give the correct answer.
There's another 200 or so puzzles, some good some not so good.
They give the correct answer.
There's another 200 or so puzzles, some good some not so good.
Place 11 cartons with the 40" side along the back of the
room, and repeat in front of this row so you have 15 rows
deep of 11 cartons wide (165 cartons). In the remaining
space, place two cartons with their 48" side against the back
and make 18 rows of these (36 cartons). This gives 165 +
36 = 201 refrigerators stored. You can also get 201 fridges in
by changing the numbers so you have 15 rows of 5 cartons
and 18 rows of 7 cartons
room, and repeat in front of this row so you have 15 rows
deep of 11 cartons wide (165 cartons). In the remaining
space, place two cartons with their 48" side against the back
and make 18 rows of these (36 cartons). This gives 165 +
36 = 201 refrigerators stored. You can also get 201 fridges in
by changing the numbers so you have 15 rows of 5 cartons
and 18 rows of 7 cartons
A photon without any luggage checks into a hotel, he's travelling light.
September 29th, 2013 at 10:54:31 AM
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Thanks, Jeepster. I hadn't discovered that second solution, and I don't think anyone else had posted it.
October 17th, 2013 at 2:39:42 PM
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Now Airline thinking as I have previously suggested involves putting an aisle in the room, thus if you think like the airline, the correct answer is as they published, because of the aisle.
And now sadly it appears Delta put an aisle in their reservation system... been doen most of this afternoon.
And now sadly it appears Delta put an aisle in their reservation system... been doen most of this afternoon.
Some people need to reimagine their thinking.
October 17th, 2013 at 3:40:35 PM
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Quote: DocRight now I am a little too lazy to check my work -- is answer E) the maximum possible if you ignore the restriction that the refrigerators must be stored upright? My initial calculation is that you could only fit 324 in the space that way, but maybe I'm wrong.
I also got 324 Doc just dividing the size of the room by the cubic feet / fridge so that would seem to be an absolute mzximum.
The restriction that the refrigerators need to be stored upright is a restriction from real life. When a fridge is laid on its side for any length of time some of the liquid refrigerant can flow into the small tubes in the evaporator. This can cause vapour locks that can take a technician to clear. The same thing can happen when you move your fridge and lie it down in a vehicle and than shake during your drive. If you ever inadvertantly do this leave the fridge standing for several hours so that the refrigerant at least has a chance to flow out again.
Be careful when you follow the masses, the M is sometimes silent.
