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# Maths illusions watch

1. Originally Posted by Zuber
here's a thread where you can post the best maths illusions. Please feel free to post illusions.

Here's mine. tell me what you think of it

a = b
times both sides by b
ab = b2
minus a2
ab – a2 = b2 – a2
factorise
a(b-a) = (b+a)(b-a)
divide by (b-a)
a = b+a
replace b by a
a = a + a
a = 2a
divide by a
1 = 2

If 1 = 2, the world would end
Tut tut. Trying to divide by zero never gets anyone anywhere... lol - quite clever though.
2. You're all confusing me and making my brain hurt
3. (Original post by * gemchicken *)
You're all confusing me and making my brain hurt
when he divided both sides by (a-b) he divided by zero as he stated that a=b
get it?
4. (Original post by Darth)
heres one (but its not really math related):
two fathers and twp sons went fishing. All of them caught 1 fish each. The total # of fish is 3. How so?
one son is also a father so there is a son, a father (who is also a son) and a grandfather!
5. (Original post by trish xx)
one son is also a father so there is a son, a father (who is also a son) and a grandfather!
right! many smart people here
6. about the half full/ half empty glass from ages ago...
its neither... the glass is twice as big as it should be.

(ENGINEERS ROCK!!!.........ahem)
7. (Original post by esx77)
you said infinity hotel has a room for every natural number so each guest can be matched to a corresponding natural number
I also said that every room is already occupied.
8. (Original post by dacb1984)
I suppose he could just get everybody to move over one room, in which case Room #1 would be free.
That works for one person... For a infinite number everyone moves to the room with double their current number, leaving all the odd numbers free - the infinite number of people move into the infinite number of odd (and empty) rooms.
9. Anyone know the one about infinity hotel?

Infinity hotel has a room for every natural number (1,2,3,...). Each room can accomodate one person. One day, every room is occupied (this is alright, because the population of the mathiverse is infinite).

Another person arrives at the hotel. How does the manager fit him in?

An infinite number of people (one for every natural number) arrive. How does the manager fit them in?

Happy puzzling!

Samuel Borin
Recreational Mathematician
How can all the rooms be occupied when there's an infinite number of rooms? You can't just say 'because there is an infinite number of people' either because clearly not every infinity is of the same 'size'.
10. It is one of those riddles where "Every" is just a name of a certain room?
11. Here is a brilliant one that I (after about 3 hours) figured out myself. Pick a number between 1-10, subtract it by itself, and the answer is 0!!!!!
12. wow FOALY,genius!
13. (Original post by dvs)
-1 = -1
1/-1 = -1/1
sqrt(1/-1) = sqrt(-1/1)
1/i = i/1
1 = i^2
1 = -1

Heh, I like this one. Took me a while to figure out the mistake.

1/i = -i, not i, so the fourth step onwards are incorrect.

Here is something stupid.

Think of a number between 1 and 10.
Times it by 9.
If the number has two digits, add these two digits together (e.g. 47 --> 4+7 = 11).
Subtract 4.
Now figure out the corresponding letter in the alphabet (e.g 1 = a, 2 = b, 3 = c etc).
Think of an animal with that letter and...

Shazamm! You are thinking of an Elephant! Probably!
14. i was thinking of an egg
15. (Original post by yo-less)
wow FOALY,genius!
Yeh I know, call it intuition if you like, but I think I am really getting the hang of this whole mathamatical subject - here's another one I worked out E=mc²

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