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Geek Culture / Maths Problem

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Libervurto
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Posted: 28th Sep 2012 20:30 Edited at: 28th Sep 2012 20:34
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Here's an interesting maths problem that occurred to me.

My bathroom is tiled with square tiles. The tiles are fairly shiny and give off a reflection. On one of the walls there is a mirror. When I stand in the middle of the room and look into the mirror, the reflection of a single tile on the opposite wall holds a reflection of almost exactly four tiles. What is the distance between the two walls in terms of tiles?

Hmm maybe this is unsolvable without accurate angles...

Shh... you're pretty.
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Diggsey
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Posted: 28th Sep 2012 21:32 Edited at: 28th Sep 2012 21:38
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It's an impossible situation - the reflection of a single tile will hold (5/3) of a tile across and (5/3) of a tile down, equal to an area of (25/9) = 2.77... tiles regardless of the size of the room.

If you instead stood at the back of the bathroom the reflection of a single tile will hold 2 tiles across and 2 tiles down, equal to an area of 4 tiles.

(as for why, just try drawing the lines of sight in MS paint)

[b]
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Bootlicker
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Posted: 28th Sep 2012 22:24
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Here's an interesting one:

I borrow £50 from ManA and £50 from ManB. So i have £100. I then spend £97 and have £3 left. I pay back £1 to each man and pocket the other pound. I now owe each man £49. Although 49+49=98. Plus my pound =99. What happened to the other one pound?

50+50 = 100.
100-97 = 3.

2*49 = 98.
98+1 = 99.

POUND MISSING.

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Diggsey
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Posted: 28th Sep 2012 23:02
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You owe the two men 98 pounds, 97 of which you spent and the other 1 you kept...

[b]
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Bootlicker
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Posted: 28th Sep 2012 23:23
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but i started with 100. and finished with 99.

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Libervurto
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Posted: 28th Sep 2012 23:47 Edited at: 29th Sep 2012 00:02
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@Bootlicker that's a much tidier version of that problem than I've heard before.

It's a mathematical error. The debt is 100. What you spend is irrelevant. You pay 2 back reducing the debt to 98. The pound you keep is debt so it's included in the remaining 98 debt.

@Diggsey
Okay if I stand at the back of the room then. So the tile in the mirror reflection appears to be two room-lengths away, and the four tiles inside the tile reflection (one of them being the tile itself) appears four room-lengths away.

Is the apparent size ratio of tiles to reflected tiles the same no matter what size the room is? What is the formula for distance perspective?

[edit] Corrected an error.

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Diggsey
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Posted: 29th Sep 2012 01:14 Edited at: 29th Sep 2012 01:14
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Quote: "but i started with 100. and finished with 99."


No you didn't, you started with 0 and ended up with 1, and there's no problem with that. The sum to 99 is meaningless.

Quote: "Is the apparent size ratio of tiles to reflected tiles the same no matter what size the room is? What is the formula for distance perspective?"


Yes, light travels in a straight line and comes to a point at the "eye" so something twice as far away will be half the size.

[b]
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ionstream
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Posted: 29th Sep 2012 05:34
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Man A = -49
Man B = -49
Store where you spent your money = +97
You = 1

The end.

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PAGAN_old
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Posted: 29th Sep 2012 09:35
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this might be a bit offtopic but, i saw a math problem in a texbook today (a photo of it uploaded to the internet).

A textbook, a notebook and a sketchpad were purchased. The total sum of the cost of all three items excluding the notebook adds up to $75. The price of the book alone is $40. What is the price of the notebook? What is the price of the sketchpad?

for some reason it seemes solvable to me so i gave it a shot. 10 minutes later i realized this problem is unsolvable.


dont hate people who rip you off,cheat and get away with it, learn from them
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Libervurto
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Posted: 29th Sep 2012 17:08
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Using only prime numbers, add them together in sequence and only note the totals that produce prime numbers. This produces the following sequence:

2 = 2
2 + 3 = 5
2 + 3 + 5 + 7 = 17
17 + 11 + 13 = 41
41 + 17 + 19 + 23 + 29 + 31 + 37 = 197
197 + 41 + 43 = 281

2, 5, 17, 41, 197, 281, ...
What is the next prime total in the sequence?


I think this sequence is interesting but I don't know if it has any novel mathematical properties.

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Indicium
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Posted: 29th Sep 2012 20:15
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Quote: "for some reason it seemes solvable to me so i gave it a shot. 10 minutes later i realized this problem is unsolvable."


It's obviously unsolvable, there's two unknowns.

40 + A + B = 75

So
A = 35 - B
B = 35 - A

Which can't be solved without knowing A or B. xD


They see me coding, they hating. http://indi-indicium.blogspot.co.uk/
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Neuro Fuzzy
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Posted: 30th Sep 2012 00:21 Edited at: 30th Sep 2012 00:47
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Key words: "Excluding the notebook"



$textbook+$sketchpad = $75

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PAGAN_old
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Posted: 30th Sep 2012 04:33
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Quote: "It's obviously unsolvable, there's two unknowns.

40 + A + B = 75

So
A = 35 - B
B = 35 - A

Which can't be solved without knowing A or B. xD
"


The strange thing is i thought i remembered, solving equesions with 2 unknowns back in highschool algebra class, but everything from that class is blurry and confusing so i cant say for sure.


dont hate people who rip you off,cheat and get away with it, learn from them
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Neuro Fuzzy
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Posted: 30th Sep 2012 04:36
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Quote: "The strange thing is i thought i remembered, solving equesions with 2 unknowns back in highschool algebra class, but everything from that class is blurry and confusing so i cant say for sure."

read my comment, it's solvable, there's one unknown.

If you have two equations and two unknowns then it might be solvable (you could phrase it in terms of invertible matrices also, if you can make an invertible matrix from the coefficients then it's solvable)

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PAGAN_old
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Posted: 30th Sep 2012 05:23
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[quote]If you have two equations and two unknowns then it might be solvable (you could phrase it in terms of invertible matrices also, if you can make an invertible matrix from the coefficients then it's solvable)[center] ok but that problem from the text book asks you to find the price of both the unknowns. But i guess you could be correct. I cant say, i kinda suck at complex math beyond very basic algebra. but sure ill believe you.


dont hate people who rip you off,cheat and get away with it, learn from them
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Neuro Fuzzy
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Posted: 30th Sep 2012 06:18
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It's not difficult, don't just believe me.

The key piece of information is that it says

Quote: "A textbook, a notebook and a sketchpad were purchased. The total sum of the cost of all three items excluding the notebook adds up to $75. The price of the book alone is $40. What is the price of the notebook? What is the price of the sketchpad?"

EXCLUDING THE NOTEBOOK.

So the price of the textbook and sketchpad is $75, the price of the textbook alone is $40, so the price of the sketchpad is $35. For the first question, we have to say, "Nothing is said about the notebook, so we don't know its price".

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Benjamin
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Posted: 30th Sep 2012 22:19
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Quote: "For the first question, we have to say, "Nothing is said about the notebook, so we don't know its price"."


So it's unsolvable etc.
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Neuro Fuzzy
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Posted: 1st Oct 2012 02:01
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meh, if that problem was on a test that would be the answer. My main point was just that Indicium's analysis was wrong.

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ionstream
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Posted: 1st Oct 2012 02:10
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If "book" means textbook then you can't answer anything except the one given. If it meant notebook then yes you can get the price of all three.

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Indicium
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Posted: 1st Oct 2012 15:09
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Quote: "My main point was just that Indicium's analysis was wrong."


Yep, didn't read the question properly. I often find that my tutors have scribbled RTFQ!! ('Read the full/****ing question' <- Haven't worked out which they mean yet. ) all over my mock papers...


They see me coding, they hating. http://indi-indicium.blogspot.co.uk/
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Seppuku Arts
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Posted: 1st Oct 2012 16:55
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If it was my old year 9 science teacher then probably the latter. You'd think she was a sailor.

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