How Many Years to Test Every Combination of a 15-Piece Molecular Puzzle?

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Discussion Overview

The discussion revolves around calculating the number of possible combinations for arranging 15 molecular pieces in a specific order, as inspired by a sci-fi narrative. Participants explore different mathematical interpretations and calculations related to permutations and combinations, specifically focusing on factorials versus exponentiation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the accuracy of the author's claim about the number of combinations, calculating 15^15 and arriving at approximately 437 quadrillion combinations.
  • Another participant suggests that if the molecular pieces must be arranged in a specific order, the correct calculation should be 15!, which equals 1,307,674,368,000 possibilities.
  • A further inquiry is made about the necessity of order in the arrangement of the molecular pieces, reinforcing the idea that 15! is the appropriate calculation if order matters.
  • A participant expresses curiosity about the factorial concept and seeks resources to understand it better, indicating interest in the underlying mathematics.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct method for calculating the combinations, with some advocating for 15^15 and others for 15!. The discussion remains unresolved regarding which calculation is appropriate based on the context provided.

Contextual Notes

There is uncertainty regarding the assumptions about whether the molecular pieces must be arranged in a specific order, which affects the choice between using factorials or exponentiation in the calculations.

SteveH66
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I am not sure if this is the right sub-forum to post this question in or not, if not I appologize for posting in the wrong place - it looked like the most likely forum to be the correct one.

In a sci-fi book I was reading, the author talked about an 'artificial symbiote' being created by 15 molecular pieces aligned correctly, which had been stolen from the villians. He said the possible combinations were in the millions, and that if you tested one combination per second, it would take over 4,000 years. This has been nagging at me for quite a while, I did what I thought was the proper calculation to find this out, to check his figures and I come up with much different numbers. So I was wondering if someone could tell me if I am not calculating this correctly.

First, I decided you would have to calculate 15 to the 15th power, 15^15, to get the number of possible combinations. When I do this, I get over 437 Quadrillion possible combinations 437,893,890,380,859,000. Next I calculated the number of seconds in a year, I got 31,536,000. Then I divided the number of calculations by the number of seconds in a year. Instead of 4,000 I got 13,885,524,174.94

13 billion is a lot different than 4,000 so I am puzzled. Am I calculating this wrong, or is the author? Thanks for any light you can shine on this problem for me.
 
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The description is a little vague.
One possible interpretation. 15 items to be placed in proper order. The number of possibilities is 15! = 1307674368000. This leads to 41000 years.
 
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Do we know how the molecular pieces are chosen to be aligned?

If they must be placed in a specific order, then the number of possibilities is 15! instead of 15^15.
 
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I don't know a lot about advanced mathematics, so I don't know what 15! is, but yes H6ss, the molecular pieces of the compound(?) must be placed in a specific order to work. If any of the 15 are out of order, the compound will not function. So it sounds like 15! would be correct as you stated it. Where would I go to find out more about 15! ? What is the name for this type of calculation? I find the math behind things like this very interesting. Thanks for the help mathman and h6ss.
 
SteveH66 said:
I don't know a lot about advanced mathematics, so I don't know what 15! is, but yes H6ss, the molecular pieces of the compound(?) must be placed in a specific order to work. If any of the 15 are out of order, the compound will not function. So it sounds like 15! would be correct as you stated it. Where would I go to find out more about 15! ? What is the name for this type of calculation? I find the math behind things like this very interesting. Thanks for the help mathman and h6ss.

n! is the factorial of n, which is the product of all positive integers less than or equal to n.

For example, 15! = 15*14*13*12*11*10*9*8*7*6*5*4*3*2*1

It is used notably in combinatorics: there are n! different ways of arranging n distinct objects into a sequence.

More information: http://en.wikipedia.org/wiki/Factorial
 
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