card trick

[weisyboy]

check this out
http://www.hondomagic.com/html/a_little_magic.htm

it is pretty clever how they trick you into thinking its just your card that has been removed.

[thesupervisor]

yes notbad they just change all the cards everytime

[pawnhead]

Mystical Ball (http://www.mysticalball.com/)

And here's a little puzzle that might make you think a bit before you 'get it':

Three men decided to split the cost of a hotel room. The hotel manager gave them a price of $30. The men split the bill evenly, each paying $10, and retired to their room.

However, the manager realized that it was a Wednesday night, which meant the hotel had a special: rooms were only $25. He had overcharged them $5!

He promptly called the bellboy, gave him five one-dollar bills and told him to return it to the men. When the bellboy explained the situation to the men, they were so pleased at the honesty of the establishment that they promptly tipped the bellboy $2 of the $5 he had returned and each kept $1 for himself.

The Problem: Each of the three men ended up paying $9 (their original $10, minus $1 back) totalling $27, plus $2 for the bellboy makes $29. Where did the extra dollar go?

[Ashore]

Mystical Ball (http://www.mysticalball.com/)

And here's a little puzzle that might make you think a bit before you 'get it':

Three men decided to split the cost of a hotel room. The hotel manager gave them a price of $30. The men split the bill evenly, each paying $10, and retired to their room.

However, the manager realized that it was a Wednesday night, which meant the hotel had a special: rooms were only $25. He had overcharged them $5!

He promptly called the bellboy, gave him five one-dollar bills and told him to return it to the men. When the bellboy explained the situation to the men, they were so pleased at the honesty of the establishment that they promptly tipped the bellboy $2 of the $5 he had returned and each kept $1 for himself.

The Problem: Each of the three men ended up paying $9 (their original $10, minus $1 back) totalling $27, plus $2 for the bellboy makes $29. Where did the extra dollar go?

same as I have 11 fingers 1,2,3,4,5 on one hadn and 10,9,8,7,6 on the other, now 6+5 =11 :rolleyes:

[pawnhead]

same as I have 11 fingers 1,2,3,4,5 on one hadn and 10,9,8,7,6 on the other, now 6+5 =11 :rolleyes:Give the man a cupie doll. :2tsup:
That just leaves the Mystical Ball to be solved. :wink:

Here's another problem:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

[NCArcher]

That just leaves the Mystical Ball to be solved. :wink:



It took me a couple of goes to get it.
There are only a few possible answers. The table of symbols changes every time so that those answers are the same symbol.
I didn't notice till i tried the same answer twice in a row. :doh:

[javali]

Give the man a cupie doll. :2tsup:
That just leaves the Mystical Ball to be solved. :wink:

Here's another problem:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Not if you're Al.

[Ashore]

Give the man a cupie doll. :2tsup:
That just leaves the Mystical Ball to be solved. :wink:

Here's another problem:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
His first choice was 331/3% chance it was No1 or the door you picked if you change, it is a 50% chance its door 2, then again it's now 50% door 1
but logic says change
As for the magic ball all the no.s 10 - 19 when added together and taken from the original will equal 9, 20 - 29 will equal 18, 30 - 39 = 25 etc so just make all these symbols the same and presto :2tsup:

[pawnhead]

It's counterintuitive, but you're actually twice as likely to win if you change doors. If you change, then your winning odds are 66 2/3 %. If you don't then you've still only got a 33 1/3 % chance.

A Proof That 2 = 1

(1) Given: ________________________ X = Y
(2) Multiply both sides by X:_________ X^2 = XY
(3) Subtract Y^2 from both sides:____ X^2 - Y^2 = XY - Y^2
(4) Factor both sides:______________ (X + Y)(X - Y) = Y(X - Y)
(5) Cancel out common factors:______ (X + Y) = Y
(6) Substitute in from line (1):________ Y + Y = Y
(7) Collect the Y's:__________________ 2Y = Y
(8) Divide both sides by Y:____________ 2 = 1

QED! !

[Alastair]

Mathematically, chance is even . Open door is empty, so must be behind one of 2, so 50% either way.

Throw in the quiz host. He knows where the prize is. He doesn't want to give up the prize, (if he is fond of his job), so opening the remaining door is a ploy to make you change, as car is behind your (already) chosen door. (makes sense to me anyway)

[Ashore]

It's counterintuitive, but you're actually twice as likely to win if you change doors. If you change, then your winning odds are 66 2/3 %. If you don't then you've still only got a 33 1/3 % chance.

A Proof That 2 = 1

(1) Given: ________________________ X = Y
(2) Multiply both sides by X:_________ X^2 = XY
(3) Subtract Y^2 from both sides:____ X^2 - Y^2 = XY - Y^2
(4) Factor both sides:______________ (X + Y)(X - Y) = Y(X - Y)
(4a) cancle out common factors___________(x+y) 0= y 0




(5) Cancel out common factors:______ (X + Y) = Y
(6) Substitute in from line (1):________ Y + Y = Y
(7) Collect the Y's:__________________ 2Y = Y
(8) Divide both sides by Y:____________ 2 = 1

QED! !

[Gra]

Sheesh.. Wheres Wongo when you need him:U:U

I think its time for a Mathematics forum :roll:

[pawnhead]

@Ashore. Bingo.
Multiplying anything by 0 is undefined. It's the same as saying 2 X 0 = 1 X 0, although it's true, you can't just take away the 0s
Mathematically, chance is even . Open door is empty, so must be behind one of 2, so 50% either way.

Throw in the quiz host. He knows where the prize is. He doesn't want to give up the prize, (if he is fond of his job), so opening the remaining door is a ploy to make you change, as car is behind your (already) chosen door. (makes sense to me anyway)Your chances are doubled to 2/3 if you change doors.



(1)Think of a number between 1 and 10.
(2)Multiply this number by 9.
(3)Add the two digits together.
(4)Subtract 5 from your answer.
(5)Associate your number with a letter from the alphabet. For example, A = 1, B= = 2, and so on.
(6)Think of a country in Europe beginning with that letter.
(7)Think of an animal where the first letter of the animals name is the last letter of the country's name. For example, England ends with "d", so you can associate that with "dog".
(8)Think of a color where the first letter of the color's name is the last letter of the animals name.

Answer (highlight) Sorry. There's no orange kangaroos in Denmark.

[Ashore]

Sheesh.. Wheres Wongo when you need him:U:U

I think its time for a Mathematics forum :roll:
could be, take a count :doh:

[Alastair]

Hi John

Sorry but logic doesn't wash. With removal of 1 door, its contribution to the possibilities become redundant, and the problem reverts to the probability of finding 1 behind 2, ie 50%.

In the absence of a distorting factor, as in the host knowing and trying to direct attention, there is an equal possibility that it is behind either door.

I would be interested to hear your justification for the 2/3 possibility, rather than the bald statement.

regards

[Ashore]

@Ashore. Bingo.
Multiplying anything by 0 is undefined. It's the same as saying 2 X 0 = 1 X 0, although it's true, you can't just take away the 0sYour chances are doubled to 2/3 if you change doors.



(1)Think of a number between 1 and 10.
(2)Multiply this number by 9.
(3)Add the two digits together.
(4)Subtract 5 from your answer.
(5)Associate your number with a letter from the alphabet. For example, A = 1, B= = 2, and so on.
(6)Think of a country in Europe beginning with that letter.
(7)Think of an animal where the first letter of the animals name is the last letter of the country's name. For example, England ends with "d", so you can associate that with "dog".
(8)Think of a color where the first letter of the color's name is the last letter of the animals name.

Answer (highlight) Sorry. There's no orange kangaroos in Denmark.

any number multiplied by 9 the digits always add up to 9
subtract 5 europian country starting with D , only one Denmark
Animal starting with K most will say Kangreoo a few koala
O only colour is orange :q

[pawnhead]

Hi John

Sorry but logic doesn't wash. With removal of 1 door, its contribution to the possibilities become redundant, and the problem reverts to the probability of finding 1 behind 2, ie 50%.It's already contributed to the problem so it's not redundant.
In the absence of a distorting factor, as in the host knowing and trying to direct attention, there is an equal possibility that it is behind either door.Certainly the absence of the host would make the whole problem redundant.
I would be interested to hear your justification for the 2/3 possibility, rather than the bald statement.

regardsI'm just giving more people the opportunity to have a think about it first. :wink:

Here's one that a teacher gave us back in my school days:

Punctuate this sentence:

"James while John had had had had had had had had had had had a better effect on the teacher."

Then try this one:

"that that is is that that is not is not is that it it is"

:think:

[Gingermick]

IIt's counterintuitive, but you're actually twice as likely to win if you change doors. If you change, then your winning odds are 66 2/3 %. If you don't then you've still only got a 33 1/3 % chance.


Ok, javali's link explains it quite well.

[javali]

Sorry but logic doesn't wash. With removal of 1 door, its contribution to the possibilities become redundant, and the problem reverts to the probability of finding 1 behind 2, ie 50%.


This is only true when the removal of the door is independent of your choice. As the removal depends on your choice the removal is not redundant.

To get some intuition into the problem, try changing the problem a bit - there are 1000 doors. You pick one, the host opens 998, showing 998 goats behind them. Is it to your advantage to switch?

For the math:
Once you chose the door there are two possible outcomes. ither you chose the door with the car, or not. The probability of the first is 1/3, and of the second is 2/3.

If you picked a door with a goat, the host has no choice of door - he picks the one door with a goat, leaving the door with the car closed.

If you picked the door with the car, regardless of which door the host opens, the other clossed door will have a goat.

Hence in 2/3 of the cases, the other door has a car, and in 1/3 it has a goat.

Edit: For more information check http://en.wikipedia.org/wiki/Monty_Hall_problem

[Alastair]

Goddit

In fact the chance of picking the car are still equal, what is not equal is that there were 2 chances to pick the oroginal goat, and thus get the double chance.