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December 31st, 2012, 3:14 pm
Forum: Brainteaser Forum
Topic: What is the probability to toss HH in 10 tosses?
Replies: 11
Views: 13328

### What is the probability to toss HH in 10 tosses?

November 25th, 2011, 7:40 pm
Forum: Brainteaser Forum
Topic: making number closest to e
Replies: 18
Views: 73102

### making number closest to e

can't be compared with the latest posts but without any tricks (other than bending the rules) we can get 6 decimal pointse ~ for k between 0 and 9.
January 20th, 2011, 8:13 pm
Forum: Brainteaser Forum
Topic: Wine & rats
Replies: 14
Views: 29535

### Wine & rats

In this version minimum 10 rats are required but for the sake of the rats you can encode it such that at most 8 will die.
January 7th, 2011, 12:33 am
Forum: Brainteaser Forum
Topic: Card Problem
Replies: 18
Views: 37207

### Card Problem

<t>The problem to find E{N} for N(52,13).let's start with a simpler case N(3,1) to enumerate all combinations (which is C(3,1)), interested face is "1" and others ".", we count the remaining cards in the deck.1.. -> 2.1. -> 1..1 -> 0Let S is the sum of all remaining cards, 3 in this caseThe number w...
February 26th, 2010, 8:45 pm
Forum: Brainteaser Forum
Topic: eigenvalue question
Replies: 6
Views: 35828

### eigenvalue question

and at that lower bound the min eigenvalue will be zero.ps. by the way that lower bound for alpha is -1/(n-1) where n is the size of the matrix.
February 22nd, 2010, 9:27 pm
Forum: Brainteaser Forum
Topic: Newborns brainteaser
Replies: 18
Views: 39793

### Newborns brainteaser

yep, the simplified formula is:p = P(boy born | boy selected) = (b + 1) / (2b + 1), where b is the number of boys initially.some special cases:b=0 -> p=1b->Inf -> p=0.5
September 8th, 2009, 8:39 pm
Forum: Brainteaser Forum
Topic: Maximum Flags
Replies: 6
Views: 36295

### Maximum Flags

Here is a solution with your notation:123147158169248259267349357368456789
September 8th, 2009, 8:10 pm
Forum: Brainteaser Forum
Topic: Maximum Flags
Replies: 6
Views: 36295

### Maximum Flags

your last two entries are not "obeying" the rule. 359369 The answer is 12.There are C(9,2) = 36 unique pairs of colors. Each flag represents C(3,2) = 3 such pairs, therefore there can be maximum 36/3 = 12 such flags.
June 15th, 2009, 8:58 pm
Forum: Brainteaser Forum
Topic: 3 dice
Replies: 3
Views: 39422

### 3 dice

More hints:For a 3 sided die (a rounded-off triangular prism will do) use these values 1,6,8b: 2,4,9c: 3,5,7here on average b beats a, c beats b, and a beats c.
June 15th, 2009, 3:57 pm
Forum: Brainteaser Forum
Topic: 3 dice
Replies: 3
Views: 39422

### 3 dice

<t>This works only for special dice. I guess it was on Scientific American some years ago. You can design the die such thata wins against b, b wins against c, and c wins against a. Note that the expected values will be the same but it's not the same as winning against.Exercise to you is to set up th...
May 13th, 2009, 8:59 pm
Forum: Brainteaser Forum
Topic: Jelly beans
Replies: 20
Views: 44435

### Jelly beans

35/16 is correct. everforget: Both can't reach to zero, when one reaches the process ends.
February 26th, 2009, 6:52 pm
Forum: Brainteaser Forum
Topic: What is the optimal strategy for this $game? Replies: 12 Views: 45224 ### What is the optimal strategy for this$ game?

February 26th, 2009, 6:51 pm
Forum: Brainteaser Forum
Topic: What is the optimal strategy for this $game? Replies: 12 Views: 45224 ### What is the optimal strategy for this$ game?

typo fixed above
December 5th, 2006, 5:35 pm
Forum: Brainteaser Forum
Topic: Sum of dices problem
Replies: 8
Views: 88613

### Sum of dices problem

well, that doesn't give you the probability.check this old post for a related Q.
October 19th, 2006, 6:02 pm
Forum: Brainteaser Forum
Topic: Interview Brainteaser
Replies: 5
Views: 91765

### Interview Brainteaser

also don't forget the option value of continuing with the game until you hit the million.
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