Math/Geometry problem! Anyone recognise this?
Discussion
My uncle and I are currently engaged in a battle of IQ one-upsmanship!
He has just said to remind him to show me "a truly baffling conundrum" (involving squares and rectangles) at dinner next week.
I've asked for a hint to what it is (so that I can rely on the internet's IQ to come across as having worked it out on the spot myself!
) and he's come back with this.
"Ooh, wouldn't you like to know... OK, it's about how the area of a square can be different from the area of a rectangle even though the parts which make up the square are identical to those which make up the rectangle."
Anyone on here recognise this problem? Even better who's got the solution to let me look like a complete genius!?
My only idea thus far, is more of a reasoning than an "answer" (if there even is one!) is:
If memory serves me right, I would assume it's because a rectangle is a quadrilateral and parallelogram, while a square is not just a quadrilateral and a parallelogram (like the rectangle), but also rhombus as well?
I guess the inter-relationship means, the maths somehow goes funny! It’s quite amazing these problems maths can post.
He has just said to remind him to show me "a truly baffling conundrum" (involving squares and rectangles) at dinner next week.
I've asked for a hint to what it is (so that I can rely on the internet's IQ to come across as having worked it out on the spot myself!
) and he's come back with this."Ooh, wouldn't you like to know... OK, it's about how the area of a square can be different from the area of a rectangle even though the parts which make up the square are identical to those which make up the rectangle."
Anyone on here recognise this problem? Even better who's got the solution to let me look like a complete genius!?
My only idea thus far, is more of a reasoning than an "answer" (if there even is one!) is:
If memory serves me right, I would assume it's because a rectangle is a quadrilateral and parallelogram, while a square is not just a quadrilateral and a parallelogram (like the rectangle), but also rhombus as well?
I guess the inter-relationship means, the maths somehow goes funny! It’s quite amazing these problems maths can post.
Edited by AdvocatusD on Friday 21st August 14:11
If a square is chopped up and made into a rectangle using all the bits, then the total areas will be the same. If it's only the total length of the edges that is preserved then you can get different areas.
Need the precise question to say how the maths works.
Need the precise question to say how the maths works.
Edited by ewenm on Friday 21st August 13:49
AdvocatusD said:
My uncle and I are currently engaged in a battle of IQ one-upsmanship!
He has just said to remind him to show me "a truly baffling conundrum" (involving squares and rectangles) at dinner next week.
I've asked for a hint to what it is (so that I can rely on the internet's IQ to come across as having worked it out on the spot myself!) and he's come back with this.
"Ooh, wouldn't you like to know... OK, it's about how the area of a square can be different from the area of a rectangle even though the parts which make up the square are identical to those which make up the rectangle."
Anyone on here recognise this problem? Even better who's got the solution to let me look like a complete genius!?
My only idea thus far, is more of a reasoning than an "answer" (if there even is one!) is:
If memory serves me right, I would assume it's because a rectangle is a quadrilateral and parallelogram, while a square is not just a quadrilateral and a parallelogram (like the rectangle), but also rhombus as well?
I guess the inter-relationship means, the math somehow goes funny! It’s quite amazing these problems math can post.
It might be something along these lines:He has just said to remind him to show me "a truly baffling conundrum" (involving squares and rectangles) at dinner next week.
I've asked for a hint to what it is (so that I can rely on the internet's IQ to come across as having worked it out on the spot myself!
) and he's come back with this."Ooh, wouldn't you like to know... OK, it's about how the area of a square can be different from the area of a rectangle even though the parts which make up the square are identical to those which make up the rectangle."
Anyone on here recognise this problem? Even better who's got the solution to let me look like a complete genius!?
My only idea thus far, is more of a reasoning than an "answer" (if there even is one!) is:
If memory serves me right, I would assume it's because a rectangle is a quadrilateral and parallelogram, while a square is not just a quadrilateral and a parallelogram (like the rectangle), but also rhombus as well?
I guess the inter-relationship means, the math somehow goes funny! It’s quite amazing these problems math can post.
http://en.wikipedia.org/wiki/Missing_square_puzzle
Also it's Maths, by the way
I remember this being on the TV. A square is cut into bits and reassembled as triangle with one less area how can this be, answer there are small gaps between the pieces of the triangle which add up to missing area.
http://en.wikipedia.org/wiki/Missing_square_puzzle
http://en.wikipedia.org/wiki/Missing_square_puzzle
Edited by voyds9 on Friday 21st August 13:54
Two things i would ask, if by the same, does he mean the perimeters are the same? If so, obviously, the areas can be different. If you have 100 1mm long sticks, you can make a several different rectangles, the one with the largest area being the square.
If you have 4 sticks of equal length, the only way to make different areas would be to move two of the sticks close to make a rectangle:
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I reckon the fomatting will get fooked, but you get the point.
I may not be thinking laterally enough however, depends what sort of puzzle it is.
If you have 4 sticks of equal length, the only way to make different areas would be to move two of the sticks close to make a rectangle:
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I reckon the fomatting will get fooked, but you get the point.
I may not be thinking laterally enough however, depends what sort of puzzle it is.
Apologies, I actually did go to school, even a rather good college!AdvocatusD said:
My uncle and I are currently engaged in a battle of IQ one-upsmanship!
He has just said to remind him to show me "a truly baffling conundrum" (involving squares and rectangles) at dinner next week.
I've asked for a hint to what it is (so that I can rely on the internet's IQ to come across as having worked it out on the spot myself!) and he's come back with this.
"Ooh, wouldn't you like to know... OK, it's about how the area of a square can be different from the area of a rectangle even though the parts which make up the square are identical to those which make up the rectangle."
Anyone on here recognise this problem? Even better who's got the solution to let me look like a complete genius!?
My only idea thus far, is more of a reasoning than an "answer" (if there even is one!) is:
If memory serves me right, I would assume it's because a rectangle is a quadrilateral and parallelogram, while a square is not just a quadrilateral and a parallelogram (like the rectangle), but also rhombus as well?
I guess the inter-relationship means, the math somehow goes funny! It’s quite amazing these problems math can post.
This one "xii. Square And Rectangle " from this page: http://www.puzzle.dse.nl/math/index_us.htmlHe has just said to remind him to show me "a truly baffling conundrum" (involving squares and rectangles) at dinner next week.
I've asked for a hint to what it is (so that I can rely on the internet's IQ to come across as having worked it out on the spot myself!
) and he's come back with this."Ooh, wouldn't you like to know... OK, it's about how the area of a square can be different from the area of a rectangle even though the parts which make up the square are identical to those which make up the rectangle."
Anyone on here recognise this problem? Even better who's got the solution to let me look like a complete genius!?
My only idea thus far, is more of a reasoning than an "answer" (if there even is one!) is:
If memory serves me right, I would assume it's because a rectangle is a quadrilateral and parallelogram, while a square is not just a quadrilateral and a parallelogram (like the rectangle), but also rhombus as well?
I guess the inter-relationship means, the math somehow goes funny! It’s quite amazing these problems math can post.
There's also a load more on there you can stump him with. I particularly like "x. Traveling Bird" from the same page.
HTH
Please report back after your Dinner with your Uncle and let us know how you got on!!
mrmr96 said:
[Please report back after your Dinner with your Uncle and let us know how you got on!!
mrmr96 thanks for that, spot on with the answer!Uncle dearest is rather deflated. It wasn't just me at dinner it turned out, so when he broke out the question, I had quick look at it along with everyone else, pronounced my inability to crack it and then let everyone talk about it till the cows came home.
Uncle said he had the answer, wasn't suprised no-one could get it, but would give everyone till the end of dinner before he divulged the answer.
Unsuprisingly, no-one had the answer, so come the end of dinner one of the guests asked to be told the answer (clearly, it was KILLING him!). My uncle then looked around the table with an expression that sort of said "so, you all admit defeat eh?" and was about to tell us what the answer was, when I chipped in with a very humble "actually, I may have an idea if you want to hear it..." Uncle looked at me and sort of handed me the paper so that I could look at it, but I waved it away with a casual, "Oh no, it's cool, I looked at it in the beginning. If I'm right it's quite a simple solution, shall I go ahead?"
I proceeded to blow him out the water with a careful analysis of the problem and how it could only be solved one way! He looked rather staggered as did the rather attractive daughter of one the guests
(who, I should add was sitting next to my fiancee)!The whole thing, the timing, the guests, the solution and the (out of character) self depracation from yours truly has had me pissing myself for a week! It was worth its weight in gold!
AdvocatusD said:
mrmr96 said:
[Please report back after your Dinner with your Uncle and let us know how you got on!!
mrmr96 thanks for that, spot on with the answer!Uncle dearest is rather deflated. It wasn't just me at dinner it turned out, so when he broke out the question, I had quick look at it along with everyone else, pronounced my inability to crack it and then let everyone talk about it till the cows came home.
Uncle said he had the answer, wasn't suprised no-one could get it, but would give everyone till the end of dinner before he divulged the answer.
Unsuprisingly, no-one had the answer, so come the end of dinner one of the guests asked to be told the answer (clearly, it was KILLING him!). My uncle then looked around the table with an expression that sort of said "so, you all admit defeat eh?" and was about to tell us what the answer was, when I chipped in with a very humble "actually, I may have an idea if you want to hear it..." Uncle looked at me and sort of handed me the paper so that I could look at it, but I waved it away with a casual, "Oh no, it's cool, I looked at it in the beginning. If I'm right it's quite a simple solution, shall I go ahead?"
I proceeded to blow him out the water with a careful analysis of the problem and how it could only be solved one way! He looked rather staggered as did the rather attractive daughter of one the guests
(who, I should add was sitting next to my fiancee)!The whole thing, the timing, the guests, the solution and the (out of character) self depracation from yours truly has had me pissing myself for a week! It was worth its weight in gold!
AdvocatusD said:
mrmr96 said:
[Please report back after your Dinner with your Uncle and let us know how you got on!!
mrmr96 thanks for that, spot on with the answer!Uncle dearest is rather deflated. It wasn't just me at dinner it turned out, so when he broke out the question, I had quick look at it along with everyone else, pronounced my inability to crack it and then let everyone talk about it till the cows came home.
Uncle said he had the answer, wasn't suprised no-one could get it, but would give everyone till the end of dinner before he divulged the answer.
Unsuprisingly, no-one had the answer, so come the end of dinner one of the guests asked to be told the answer (clearly, it was KILLING him!). My uncle then looked around the table with an expression that sort of said "so, you all admit defeat eh?" and was about to tell us what the answer was, when I chipped in with a very humble "actually, I may have an idea if you want to hear it..." Uncle looked at me and sort of handed me the paper so that I could look at it, but I waved it away with a casual, "Oh no, it's cool, I looked at it in the beginning. If I'm right it's quite a simple solution, shall I go ahead?"
I proceeded to blow him out the water with a careful analysis of the problem and how it could only be solved one way! He looked rather staggered as did the rather attractive daughter of one the guests
(who, I should add was sitting next to my fiancee)!The whole thing, the timing, the guests, the solution and the (out of character) self depracation from yours truly has had me pissing myself for a week! It was worth its weight in gold!
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