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01-15-2017 , 01:52 AM
#1
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Please forgive me, this is not exactly a probability question but I thought you would provide the best answer.

Lilliputians and Brobdingnagians can interbreed.

1) Evertually, can an individual become exactly 1% Lillipution?

2) If so, how many generations would it take?
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01-15-2017 , 03:01 AM
#2
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As a rule we do not simply provide answers to these types of questions.

Folks here are generally helpful, so we are happy to help you find the answer.

If you would like guidance, help, and assistance, why don't you tell us what you have done so far?

Have you manually determined what "mixes" are possible after one generation, two generations, three generations, etc.?

If so, have you discovered any "pattern" to what "mixes" are possible after N generations?

That should be enough to answer the question.
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01-16-2017 , 12:57 AM
#3
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Mod edit: I hope you don't mind but I am going to place your reply in a spoiler. The question is not difficult and if OP (or anyone else) wants to solve it himself, the hint in post #2 is sufficient. If OP (or anyone else) wants to see the answer straight away, he can click on the spoiler.

Spoiler:

This question is equivalent to asking if there are any two positive integers, A and N, such that:

0.01 = A * 2-N

The answer is no. Decompose 0.01 into its prime factors:

1/(2252) = A * 2-N

2N-2/52 = A

Since 2 and 5 are prime, no power of 2 can be evenly divided by a power of 5, so there is no integer solution.

Last edited by whosnext; 01-16-2017 at 01:18 AM. Reason: added spoiler and mod edit
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01-16-2017 , 04:06 AM
#4
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Don't need these fancy letters and symbols. Its obvious that your fraction of each type can be turned into a fraction with an integer numerator and a denominator that is a power of two. But for that fraction to be exactly 1% the denominator must end in two zeros which it never will.
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01-17-2017 , 11:15 AM
#5
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You guys came up with some interesting ways of being wrong.

http://www.bbc.co.uk/news/magazine-28986843
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