Puzzle

A couple of good explanations, but here's another way of looking at it:

If there're 1000 doors, you picked one. There's a 1/1000 chance of it being the right door. The host now has to open 998 of the 999 doors remaining, showing you the empty rooms.

The other 999 doors have a combined probability of 999/1000. The host's actually forced to leave one door closed for you. The remaining door still have the probability of 999/1000 of being the prize door, since the combined probability of the group of 999 doors containing the prize door hasn't changed, but you're left with just one door in that group.

The tricky part of the puzzle is the fact that it's 3 doors, with host opening 1 empty door, rather than "leave only one door by opening empty doors only".
 
Here's another good puzzle:

Proof That 2 = 1
X = Y Given
X^2 = XY Multiply both sides by X
X^2 - Y^2 = XY - Y^2 Subtract Y^2 from both sides
(X+Y)(X-Y) = Y(X-Y) Factor both sides
(X+Y) = Y Cancel out common factors
Y+Y = Y Substitute in from line 1
2Y = Y Collect the Y's
2 = 1 Divide both sides by Y
 
thesubstitute said:
Here's another good puzzle:

Proof That 2 = 1
X = Y Given
X^2 = XY Multiply both sides by X
X^2 - Y^2 = XY - Y^2 Subtract Y^2 from both sides
(X+Y)(X-Y) = Y(X-Y) Factor both sides
(X+Y) = Y Cancel out common factors
Y+Y = Y Substitute in from line 1
2Y = Y Collect the Y's
2 = 1 Divide both sides by Y
Click to expand...

dividing by zero :o
 
Here's a long winded one but here goes anyway:

Three men arrive at a hotel in need of a room. The desk clerk explains that they only have one room available, and they'd have to share. The price is £30. The men agree, and each pay £10 and head up to the room. Later on, the desk clerk realises he's overcharged them, and the price of the room is actually only £25. So he gives the bellboy £5 to take up to the men. On the way the bellboy realises there's no way to split £5 three ways, so he figures he'll save them the hassle and give them £3, and pocket the remaining £2 for himself. So if each man has now paid £9 totalling £27, and the bellboy has £2 making it £29, where did the other pound go?
 
thesubstitute said:
Here's another good puzzle:

Proof That 2 = 1
X = Y Given
X^2 = XY Multiply both sides by X
X^2 - Y^2 = XY - Y^2 Subtract Y^2 from both sides
(X+Y)(X-Y) = Y(X-Y) Factor both sides
(X+Y) = Y Cancel out common factors
Y+Y = Y Substitute in from line 1
2Y = Y Collect the Y's
2 = 1 Divide both sides by Y
Click to expand...

You're dividing by x-y, which is 0.
That's an old one ;)

Edit: Beaten!!
 
Steve2000 said:
Here's a long winded one but here goes anyway:

Three men arrive at a hotel in need of a room. The desk clerk explains that they only have one room, and they'd have to share. The price is £30. The men agree, and each pay £10 and head up to the room. Later on, the desk clerk realises he's overcharged them, and the price of the room is actually only £25. So he gives the bellboy £5 to take up to the men. On the way the bellboy realises there's no way to split £5 three ways, so he figures he'll save them the hassle and give them £3, and pocket the remaining £2 for himself. So if each man has now paid £9 totalling £27, and the bellboy has £2 making it £29, where did the other pound go?
Click to expand...

Deceptive puzzle:

Each paid £9 in the end, comes to £27, clerk pockets £2, so subtract that not add it and the £25 was rent.
 
Another puzzle since the 2=1 one was immediately solved :<

This one will probably take some explaining along with answer! (yeah, please explain rather than just shouting out colour)

A king wants his daughter to marry the most logical of 3 intelligent princes, and so comes up with a test for them.

The princes are gathered into a room and seated, facing one another, and are shown 2 black hats and 3 white hats. They are blindfolded, and 1 hat is placed on each of their heads, with the remaining hats hidden in a different room.

The king tells them that the first prince to correctly identify the color of his hat will marry his daughter. A wrong guess will mean death.

The blindfolds are then removed. You are one of the princes, you see 2 white hats on the other prince's heads. What color is your hat?
 
Steve2000 said:
Here's a long winded one but here goes anyway:

Three men arrive at a hotel in need of a room. The desk clerk explains that they only have one room available, and they'd have to share. The price is £30. The men agree, and each pay £10 and head up to the room. Later on, the desk clerk realises he's overcharged them, and the price of the room is actually only £25. So he gives the bellboy £5 to take up to the men. On the way the bellboy realises there's no way to split £5 three ways, so he figures he'll save them the hassle and give them £3, and pocket the remaining £2 for himself. So if each man has now paid £9 totalling £27, and the bellboy has £2 making it £29, where did the other pound go?
Click to expand...

worst one ever.

The men pay £10 each, to make £30

They get £3 back which means they've paid £27

But they've overpaid by £2 now because the room actually only cost them £25

Where has the extra £2 gone? Oh yeah that's right the bellboy kept it for himself!

(The bellboy's £2 don't add to the £27 to try and make £30 - it subtracts from the £27 to make £25)
 
thesubstitute said:
Another puzzle since the 2=1 one was immediately solved :<

This one will probably take some explaining along with answer! (yeah, please explain rather than just shouting out colour)

A king wants his daughter to marry the most logical of 3 intelligent princes, and so comes up with a test for them.

The princes are gathered into a room and seated, facing one another, and are shown 2 black hats and 3 white hats. They are blindfolded, and 1 hat is placed on each of their heads, with the remaining hats hidden in a different room.

The king tells them that the first prince to correctly identify the color of his hat will marry his daughter. A wrong guess will mean death.

The blindfolds are then removed. You are one of the princes, you see 2 white hats on the other prince's heads. What color is your hat?
Click to expand...

If my hat was black and the other two princes had white hats, prince 2 would answer immediately that his hat was white, as the prince 3 didn't answer immediately, therefore prince 2 did not have a black hat. Since nobody answered immediately, I shall assume all three hats are white.
 
Steve2000 said:
If my hat was black and the other two princes had white hats, prince 2 would answer immediately that his hat was white, as the prince 3 didn't answer immediately, therefore prince 2 did not have a black hat. Therefore, all three hats are white.
Click to expand...

Very vague explanation - "who's prince 2, who's prince 3?" They both would see the same thing as well.
 
I am prince 1, the other two are 2 and 3 respectively. If two of us had a black hat, then the one with the white would know immediately, as there are only two black hats. This applies to all three princes. Since nobody chirped up immediately, that means that nobody must be wearing a black hat, as prince 1 would know from neither prince 2 or 3 answering immediately, and princes 2 and 3 would know from neither prince 1 or prince 2 answering immediately.

This becomes more complicated the more I talk about it.
 
Steve2000 said:
I am prince 1, the other two are 2 and 3 respectively. If two of us had a black hat, then the one with the white would know immediately, as there are only two black hats. This applies to all three princes. Since nobody chirped up immediately, that means that nobody must be wearing a black hat, as prince 1 would know from neither prince 2 or 3 answering immediately, and princes 2 and 3 would know from neither prince 1 or prince 2 answering immediately.

This becomes more complicated the more I talk about it.
Click to expand...

You didn't really go into the seeing 1 white 1 black situation, which you kinda started with but didn't go into. Note that two black hats situation can't exist since you're already seeing two whites anyway.

Anyway, say Prince 1 has a black hat, that prompts prince 2 and 3 to see 1 black 1 white.

This is the point that both princes would wait and see if the other prince would shout 1 in case they see two blacks.

If they didn't shout, it'll mean they'd both know that they have a white hat on.

So in the case where Prince 1 has a black hat, prince 2 and 3 will always be able to tell their own hat colour before Prince 1. When they're able to identify their own hats, Prince 1 will in turn know that he's got a black hat afterwards.

If none of them shouts, it's because Prince 1 has a white hat.
 
thesubstitute said:
Another puzzle since the 2=1 one was immediately solved :<

This one will probably take some explaining along with answer! (yeah, please explain rather than just shouting out colour)

A king wants his daughter to marry the most logical of 3 intelligent princes, and so comes up with a test for them.

The princes are gathered into a room and seated, facing one another, and are shown 2 black hats and 3 white hats. They are blindfolded, and 1 hat is placed on each of their heads, with the remaining hats hidden in a different room.

The king tells them that the first prince to correctly identify the color of his hat will marry his daughter. A wrong guess will mean death.

The blindfolds are then removed. You are one of the princes, you see 2 white hats on the other prince's heads. What color is your hat?
Click to expand...

It is most likely to be white unless the other princes are not as clever/logical and missed a chance to win the princess ;)

Two outcomes:

Your hat is black

You see two white
Prince1 sees one white and one black
Prince2 sees one white and one black

Prince1 knows that yours is black, and he can work out that his must be white, because if it was black, then prince2 would see two black hats and immediately say his was white.

The same applies to prince2.

So if yours was black, then there was no way you could win (logically), because prince1 and prince2 should both be able to work out that their hat is white, based on the fact that if either of theirs was black, then the other one would see two black hats and instantly know his must be white.


Your hat is white

If it was black, you'd have lost to one of the other princes before you could have had a 'safe' guess, so as they haven't guessed yet, your hat must be white as well. Ie you are all in the same situation, all looking at 2 white hats.
 
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