Puzzles, puzzles, puzzles?

1) 9@7 = 144

2) you left one apple in the basket when you handed it to that friend

3) p(picking a bag at random that contains white marbles) * p(choosing a white marble on your first draw) = (2/3) * (3/4) = 1/2.

Now, of the four possible choices remaining in the bags, one is impossible--drawing a white marble from the bag containing mixed marbles. This leaves 3 possibilities, two of which have white marbles.

p(drawing a white marble on the second draw) = 1/2 * 2/3 =

p(drawing a white marble on the second draw after having drawn a white marble the first time) = 1/3.

4) it was the "gun" on the end of the hose attached to the water spout

5) she grabs a stick, lights it on fire, and begins another fire to the west of the first fire. As this second fire burns westward, she walks in that direction. The first fire reaches the already-burned area and fizzles out, leaving her unharmed.

Puzzles from Cassandra

Puzzles, puzzles, puzzles?

1.

Got this one yesterday and I was told that only people with IQ over 120 can work it out.

I have changed it slightly - The one I was given had "+" signs, but I have changed that to an @ symbol to represent some function - it makes more sense that way.

1)

IF:

2 @ 3 = 10 = (2 + 3) * 2

7 @ 2 = 63 = (7 + 2) * 7

6 @ 5 = 66 = (6 + 5) * 6

8 @ 4 = 96 = (8 + 4) * 8

THEN

9 @ 7 = (9 + 7) * 9 = 16 * 9 = 144 <-----

2

I have 10 friends, each who desires an apple. I have 10 apples in a basket. I start handing out the apples...

Soon each of my 10 friends has an apple, yet 1 apple remains in the basket, how is this possible?

One of them already had an apple.

2.

I have 3 bags, one containing 2 black balls, another with 2 white balls, and the third with 1 black and 1 white. If I choose a bag at random and pull out a white ball, what is the probability that the other ball in that bag is white?

The black-black bag has been ruled out. She originally had a 2-1 chance of picking a white from the white bag. That means that before the choice and assuming that the black - black is ruled out, she was twice as likely to get a white ball from the white-white bag as the black-white bag.

That is still the case, she had a 2/3 chance of picking a white ball from the white white bag, and that fact has not changed. The probability that the other ball in the bag is white is (2/3) or 0.666666667.

3.

A man walks into a bar and asks for a glass of water

The bar tender pulls out a gun and points it at him

The man says "thanks" and walks out

Why?

It was a squirt gun

4.

A woman is lost on an island, due to cliffs surrounding the island and a lack of climbing equipment there is no way off the island. A strong wind is blowing from the west. Lightening strikes and starts a fire on the western side of the island, but the rescue plane wont be there for a few more days!!! The woman has no water or any other way of putting out the fire, so the whole island IS going to burn. How can she survive (NO she can't dig a hole either to avoid the fire!!!)????

I would love to hear any creative solutions. Will post additional details with the answers if no one works them out.

I would get to the side of the cliffs and head wet hoping to get to the burned out space at the west end of the island before the fires had spread to the side that I chose, which would be based on my location and the location of the fire .

.

I have 3 bags, one containing 2 black balls, another with 2 white balls, and the third with 1 black and 1 white. If I choose a bag at random and pull out a white ball, what is the probability that the other ball in that bag is white?

I see a lot of people answering 1/3 this is wrong. the bag with the black marbles plays no part in this problem whatsoever because you can never draw a white marble out of it in the first place and the problem is only concerned with the subset of possibilities where you randomly selected a bag that on first draw yielded a white marble. Additionally the random bag which you settle on that must yield a white marble 2/3 of the time will be the bag with two white marbles and that is the only case in which you can draw a further white marble from a bag so the answer is 2/3.

1. Formula is for @ is a @ b = a(a+b) so Answer is 144.

2. one of the friend gets the apple with the basket.

3. The probability is 1/2. Because it all comes down to whether she has the bag with 1 white + 1 black balls or the bag with 2 white balls. Its either going to be white or black.

Using probability formula Probability for white: 1/2 * 1

Probability for bag with black: 1/2 *0

Add those up you get 1/2.

The bag with 2 black bags shouldn't be considered as one event has already happened.

4. The person who goes to bar is having hiccups, looking the gun he is shocked n scared and hence cured.

5. Swim over to the west side where fire has already done the damage, use coal to purify water for survival. I guess the 'Man vs Wild' or 'Expedition Africa' used this method.

Well, I now have three of them.

1. The pattern is: Add the

two numbers together

and multiply the result

by the first number.

In other words, a@b = a(a+b)

So 9 + 7 = 16

9*16 = 144

so 9@7 = 144.

3. The gun was a squirt gun filled with water!

Update: I still think this is a plausible answer.

2. I have 3 bags, one containing 2 black balls, another with 2 white balls, and the third with 1 black and 1 white. If I choose a bag at random and pull out a white ball, what is the probability that the other ball in that bag is white?

Solution:

The probability of choosing a particular bag is 1/3.

If we choose bag no. 1, the probability of getting

any white ball is 0.

If we choose bag no.3 and pull out a white

ball, the probability that the other ball in that

bag is white is 0.

Finally, if we choose bag no.2, and pull out

a white ball, the probability that the other

ball in that bag is white is 1.

So the overall probability of the event

in question is 1/3*1 = 1/3.

2 He had one in his hand too? Or had an extra one anywhere but in the basket. One of the friends could have already had one.

2. 2/3. Two out of three times youl will have chosen the bag with two white balls and the other ball is always white. One out of three times you will have chosen the bag with only one white ball. The other is black.

4. Does she have the means to start a fire? Assuming the flames only travel East because of the wind and there's enough time for the fire to burn out, she can start her own fire to burn the East side of the island. Then when the fire goes out and it cools down she can stay on the burned out part. The air might be a bit hard to breath from the smoke though.

4 Birds 3 Flowers

The first three puzzles are pretty easy and have been solved by guys and I don't want to re-answer them here but, the fourth one is relatively challenging and none of the guys have offered a true answer. Here is my answer to the fourth question:

The woman will survive anyway, because it says somewhere in the puzzle that: "A strong wind is blowing from the west.", it never says it blows from the west to the east, it could blow from the west to the south or from the west to the north which in both cases won't harm the woman whatsoever.

Another way of working out this puzzle could be this:

When it says "Lightening strikes and starts a fire on the western side of the island", here THE WESTERN SIDE OF THE ISLAND could be the western side of the island to someone who is looking at this island from the north of this island, facing southwards (Einstein's Theory of Relativity says everything is relative, even the directions. Something which is north to you might be south to me). So the fire, considering the direction of the wind, could have no effect on the woman.

3. The man had hiccups and since the glass of water wouldn;t work, the gun scared him out of it

q2a

the last friend gets their apple in the basket (as a reward for their patience).

q2b

2/3

q4

she runs quickly and starts a fire on her own at the eastern part of the island. when the accidental fire finally reach her in the east, there's nothing left for that fire to burn off on so it will die down on its own.

oh yes. she took a long, thin branch from one of the not-yet-burned trees, lighted it off on one end from the accidental fire, ran with the 'torch' and went to burn the east.