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#26 Help Me ! » Maximize investment » 2016-04-26 05:26:44
- salem_ohio
- Replies: 9
We are planning to invest 60000$ to a bank that yields 30% (expected return after one year), bonds that yield 40% and stocks that yields 90%. We know in advance, however, that 2 of the above 3 investment choices will go bankrupt at some point before year-end but we don't know which ones. This, of course, will result to total loss of any amount that has been invested in each of these two options, along, of course with any earnings. Knowing this, our investment consultant suggested that we build a balanced portfolio so as to spread the risk and ensure some guaranteed profit.
What is the maximum guaranteed profit we can achieve?
#27 Puzzles and Games » Prisoners and hats - one more variation » 2016-04-24 08:37:00
- salem_ohio
- Replies: 10
Five prisoners are arrested for a crime. However, the jail is full and the jailer has nowhere to put them. He eventually comes up with the solution of giving them a puzzle so if they succeed they can go free but if they fail they are all executed.
The jailer gives all the prisoner party hats: He gives each prisoner one hat, which can be of any of the following colors: Cyan, Magenta, Yellow, Red, Green. Given that there are more than 5 hats of each color, it is possible that more than one prisoners wear hats of the same color.
Each of the prisoners only see the hats of the others but not on himself.
If any prisoner can figure out and say to the jailer what color hat he has on his head with 100% certainty, all five prisoners go free. If any prisoner suggests an incorrect answer, all five prisoners are executed. Communication among the prisoners is allowed only before they put the hats on and is prohibited afterwards. They all write their guess on a piece of paper simultaneously, without anyone reading each other's guess.
What strategy must they follow so as to go free?
#28 Help Me ! » Defective board » 2016-04-07 07:09:49
- salem_ohio
- Replies: 4
We have an 8x8 square board with one block being painted green, while all the others are red. We cut this board into pieces in such a way, so as to be able to reassemble the board from these pieces and reposition the green square to any of the 64 positions of the new board. How many pieces do we need at minimum and of what shape?
#29 Re: Help Me ! » Guess the coins » 2016-03-29 07:14:05
Not necessarily
Must the cardinality of the 2 subsets equal 10?
#30 Help Me ! » Guess the coins » 2016-03-29 02:16:37
- salem_ohio
- Replies: 18
Two friends, Alexander and Byron, play the following game: they have 10 coins in a row in front of them and Alexander secretly selects two consecutive coins. Byron defines two subsets of the 10 coins which he presents to Alexander. Then Alexander tells Byron how many of the coins that he chose belong in each of the two subsets (for example, 2 coins in the 1st subset and none in the 2nd). Then Byron must guess, only by one attempt, the two coins that Alexander selected. Find a strategy such that Byron always wins.
#31 Re: Help Me ! » Train to Dawanglu » 2016-03-20 20:35:11
Hi Bobby,
What if we want to solve it using probabilities? (because your solution doesn't help me understand the logic!)
Thank you!
#32 Re: Help Me ! » Train to Dawanglu » 2016-03-18 02:22:44
How??? FYI I don't know the answer 
True enough, I can work on it though. I am getting a probability of about .47
#33 Re: Help Me ! » algebra » 2016-03-14 04:26:00
4. f(a)=3 for a=13/3
#34 Re: Help Me ! » Train to Dawanglu » 2016-03-12 10:14:32
Yes
If they miss the first train is another coming?
#35 Re: Help Me ! » Train to Dawanglu » 2016-03-12 07:03:08
Not necessarily, there is also a chance it does not come, with a probability of 30%. It may come in the next minute, or even after some minutes.
Every minute there is a 70% probability for the train to come
Does this not imply that the trains are expected one a minute?
#36 Re: Help Me ! » Train to Dawanglu » 2016-03-11 21:34:28
We don't know the exact time - it can be any time, with 70% probability.
Does the first train come at 8:00 or 8:01?
#37 Help Me ! » Train to Dawanglu » 2016-03-11 21:13:34
- salem_ohio
- Replies: 24
Two chinese boys, Aiguo and Chi, arrive at the Dongdan subway station at 8:00 am and wait for the train to Dawanglu, to go to school. Every minute there is a 70% probability for the train to come, but every time the train stops at the station, there is also a 60% probability the two guys miss it, as they are abstracted and playing with their mobile phones.
What is the probability they catch the train by 8:05 am (or, to be more precise, to catch "some" train by 8:05)?