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Brain Teaser Solver

by Rodolphe Sitter

30 Mar 2009 (Updated 30 Mar 2009)

Code covered by the BSD License

Brain Teaser Solver: Compute the expected time to get a given sequence of independent outcomes.

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Description

The function OutcomeSequence.m solve brain teasers such as:

1. You toss a coin, what is the expected number of tosses for you to get the sequence 'Tails-Heads-Tails' ?

2. You throw a dice, what is the expected number of throws for you to get the sequence '1, 2, 3, 2, 1' ?

3. You randomly hit your keyboard, what is the expected number of keys you have to hit to get the sequence 'ABRACADABRA' ?

4. You play one poker game everyday. Assume you are likely to win 1 out of 4 games you play. What is the expected number of days you have to play to win 3 times in a row ?

Function details:
OutcomeSequence(Sequence, N_Outcomes)

Inputs:
- Sequence: sequence (row vector) of numbers representing the different possible outcomes. The occurrence times of those outcomes are assumed to be I.I.D. random variables, i.e. the outcomes occur independently of each other and are equally likely to happen.
- N_Outcomes: number of different possible (independent) outcomes.

Output:
- Expected_Time: expected time to get the input sequence of outcomes. This time would correspond to a number of tosses of a coin, throws of a dice and so on depending on the problem considered.

MATLAB release

MATLAB 7.5 (R2007b)

Tags for This File
Everyone's Tags	brain teaser, coin, dice, game, iid, outcome, random time, sequence
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Updates
30 Mar 2009	more examples in comments

Tag Activity for this File
Tag	Applied By	Date/Time
sequence	Rodolphe Sitter	30 Mar 2009 15:12:34
outcome	Rodolphe Sitter	30 Mar 2009 15:12:34
dice	Rodolphe Sitter	30 Mar 2009 15:12:34
coin	Rodolphe Sitter	30 Mar 2009 15:12:34
random time	Rodolphe Sitter	30 Mar 2009 15:12:34
iid	Rodolphe Sitter	30 Mar 2009 15:12:34
game	Rodolphe Sitter	30 Mar 2009 15:12:34
brain teaser	Rodolphe Sitter	30 Mar 2009 15:12:34

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