I got the first one--am pasting my answer below. I'll be back when I get the others.
Edit: OK, I got the second one.
Edit: Got them all! 10 points please?
"Water or Wine?
Two identical jars contain one wine and the other water. A beaker is used to first transfer some wine to water. The mixture is thoroughly mixed and then the beaker is used to transfer this mixture to the jar containing wine. Now, is there more wine in water or water in wine?"
They have the same amount. Think of it this way. Say you have 1000 mL of each liquid and you transfer 100 mL of water to the wine. You then mix the water in and transfer 100 mL back to the water jar. Of this, some amount x is water and the rest is wine. So the wine jar contains 1000 mL wine plus 100-x mL water, minus 100-x mL wine: 900 + x mL wine and 100 - x mL water The water jar holds 1000 mL water, minus 100 mL, + x = 900 + x mL water and 100 - x mL wine. So they're the same.
“Can you find the object with abnormal weight from 9 identical objects,using a common balance,in only three weighings?
You can use a balance, which will be horizontal when the weights on either side are balanced, and otherwise tip to the side which weighs more. Using just this balance, you win if you find the one that's different, and if it weighs more or less than the others! Remember, you can only weigh thrice.”
Call them objects 1-9. Weigh 1-3 against 4-6. If they balance, the odd one is in 7-9. Weigh 7 against 8. If they balance, the odd one is 9 and you can weigh it against a normal one to see if it's light or heavy.
If 7 and 8 don't balance, weigh the light one against a normal object. Then if they don't balance, the light one is odd and light, and if they do, the heavy one from the previous weighing is odd and heavy.
If the first weighing doesn't balance, it gets complicated. Say for the sake of argument that 1, 2, and 3 are light. Weigh 1, 2, and 4 against 3, 7 and 8. If they balance, the odd one is 5 or 6 (the two you removed from the scale) and heavy, and you can tell which by weighing them. If 3, 7 and 8 are light, the odd one is either 3 and light or 4 and heavy, and you can find out which by weighing one of them agains a normal object. If 1, 2 and 4 are light, the odd one is either 1 or 2 and it's light, so weigh them against each other to find out which one.
Incidentally, I could have done this with 12 items. It's not that much harder.
“To Switch or Not to Switch that is the question !!!
Two jokers and a king are placed face down.You are asked to choose a card. The chance of this card being a king is 1 in 3. Let's say you chose a card and then i upturned the joker. Given the option, would you switch cards now and choose the other card, to have a higher chance of picking up the king?”
Let's look at the probabilities from the beginning. There's a 33% chance that you could chose the king, a 33% chance for one Joker (call it J1) and a 33% chance for the other (J2).
For each of these choices, we next examine the probability of the dealer turning the other two cards. If you picked the King, there's a 50% chance for J1 and a 50% chance for J2, but if you picked a Joker, there's a 100% chance that the dealer will turn over the other one (since he can't turn over the King).
So the four possible sequences, with their probabilities, are:
K, J1, 16.7 %
K, J2, 16.7 %
J1, J2, 33.3%
J2, J1, 33.3%
Now, suppose that in fact, J1 has just been flipped by the dealer. That eliminates two possibilities, and makes the other two each twice as likely:
K, J1, 33.3%
J2, J1, 66.7%
In other words, you're twice as likely to have chosen the Joker as the King. So it's better to switch cards.
2007-04-18 06:31:39
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answer #2
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answered by Amy F 5
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