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by montecristo
May 12th, 2009, 8:23 am
Forum: Brainteaser Forum
Topic: Prisoners and hats
Replies: 17
Views: 52802

Prisoners and hats

That's it!
by montecristo
May 11th, 2009, 7:45 am
Forum: Brainteaser Forum
Topic: Prisoners and hats
Replies: 17
Views: 52802

Prisoners and hats

Nobody?Hint: The solution is: N-1 prisonners can be free!
by montecristo
May 8th, 2009, 8:09 am
Forum: Brainteaser Forum
Topic: Prisoners and hats
Replies: 17
Views: 52802

Prisoners and hats

<t>I dont know if you have seen this one, it is a generalisation of a classical brainteaserSuppose you have N prisoners, sentenced to death (tomorrow). But the king (who likes brainteasers) gives them a last chance: Tomorrow, every prisoner will have a colored hat, and there is M possible colors. Ev...
by montecristo
May 7th, 2009, 2:01 pm
Forum: Brainteaser Forum
Topic: Million dollars contract
Replies: 4
Views: 40745

Million dollars contract

<t>To be more precise: The stock is 10$ today. when the stock reachs 100$ it will be splited in 5. Strating from 20, when it reachs 200 it will be splitted in 5. Starting from 40, when it reachs 400 it will also be splitted in 5,...........cm27874, you have a little mistake in your proofHow much wou...
by montecristo
May 7th, 2009, 8:34 am
Forum: Brainteaser Forum
Topic: Million dollars contract
Replies: 4
Views: 40745

Million dollars contract

<t>One of your friends is the owner of a newly Wall Street coted Start Up (worth 10$ today). You think that his start up will be a very good investment. So he proposes to you the following contract: You give him today 200$, and if in the futur the stock reachs 500$, he will give you one million doll...
by montecristo
May 6th, 2009, 8:12 am
Forum: Brainteaser Forum
Topic: A new dice brainteaser
Replies: 13
Views: 44286

A new dice brainteaser

<t>A harder questionCan anyone generelize the probleme to n dimension? i.e. : you are playing a lotery where the result is a random number between 1 and n (uniform distribution). You play without paying n times, but you have to continue untill you have all the n numbers, and at every step k you pay ...
by montecristo
May 6th, 2009, 7:49 am
Forum: Brainteaser Forum
Topic: A new dice brainteaser
Replies: 13
Views: 44286

A new dice brainteaser

<t>ynotredrum:To see why do we have to calculate E(N(N+1)/2 - 21) , think about a Monte Carlo estimation: On every path i, you need N(i) throws to get all the six numbers. After N(i) throws, you pay (7+8+...+N(i))$, which is equal to N(i)(N(i)+1)/2 - 21 . Taking the average, you get the expectation ...
by montecristo
May 5th, 2009, 3:50 pm
Forum: Brainteaser Forum
Topic: A new dice brainteaser
Replies: 13
Views: 44286

A new dice brainteaser

<t>I dont think so daveangelLet N be the number of throws to get all six numbers. The probleme is about calculating (E(N(N+1)/2)-21) which is greater than ((E(N)²+E(N)/2)-21)MCarreira reminds that E(N)=14.7, so what we are calculating must be greater than 94.395I find (using a closed formula) 113.89...
by montecristo
May 5th, 2009, 2:10 pm
Forum: Brainteaser Forum
Topic: A new dice brainteaser
Replies: 13
Views: 44286

A new dice brainteaser

I dont think so14.7 is the average number of throws to get all the six numbersHere you pay 7 at the seventh level, 8 at the eighth tevel....N at the Nth levelIntuitively, this numer must be about (7+8+9+10+11+12+13+14) which is much more greater than 14.7
by montecristo
May 5th, 2009, 12:08 pm
Forum: Brainteaser Forum
Topic: A new dice brainteaser
Replies: 13
Views: 44286

A new dice brainteaser

<t>Imagine you are playing the following die game against 1 player: He gives you N dollars, and you throw a die 6 times. If you get all the six numbers you win the N$. Otherwise, you have to pay the player 7$ then throw the die. You continue till having all the six numbers, and at every step k you h...
by montecristo
April 30th, 2009, 7:59 am
Forum: Brainteaser Forum
Topic: Find the Bonus
Replies: 3
Views: 41477

Find the Bonus

That's right!I did it using Excel after reducing the possible sums to {11,17,23,27,29,35,37,41,47,53} which makes the solution much easier
by montecristo
April 29th, 2009, 11:24 am
Forum: Brainteaser Forum
Topic: Find the Bonus
Replies: 3
Views: 41477

Find the Bonus

<t>The Head of Quant research meets two junior (A and B) quants to announce their bonuses (expressed in k$). They now that they are between 2 and 100. He gives the product to A and the sum to B. A says: "I don't know what are the two bonuses"B replays: "I knew you would not know"Then A says: " Now I...
by montecristo
April 28th, 2009, 12:42 pm
Forum: Brainteaser Forum
Topic: Roll A Die Till You Get All Six
Replies: 16
Views: 50521

Roll A Die Till You Get All Six

I have coded a MC and an exact formula (recursive calculus)The MC with 1M simulations gives 26.228The exact formula gives = 26.2351... = 1315957/50160 (the same result as in wileysw's calculus, but with a different formula)
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