What is the Pattern of Number Combinations and Sums When Extracting Digits?

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SUMMARY

The discussion centers on the extraction of 2-digit numbers from unique 3-digit combinations, specifically focusing on the patterns and sums of these numbers. Each unique 3-digit number generates six distinct 2-digit permutations, as indicated by the permutation formula nPr. The conversation highlights the need for clarity regarding how to count these permutations and their resultant sums, emphasizing that the maximum number of different sums is determined by the combination formula nCr, where r equals 2.

PREREQUISITES
  • Understanding of permutations and combinations, specifically nPr and nCr.
  • Basic knowledge of factorial calculations.
  • Familiarity with the concept of unique digit extraction from numbers.
  • Ability to analyze numerical patterns and sums.
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  • Research the mathematical principles behind permutations and combinations, focusing on nPr and nCr.
  • Explore factorial calculations and their applications in combinatorial mathematics.
  • Investigate numerical pattern recognition techniques in combinatorial contexts.
  • Learn about the implications of unique digit extraction in number theory.
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Mathematicians, educators, students studying combinatorics, and anyone interested in numerical pattern analysis and permutations.

Stef Pieterse
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Hi
If i have many 3 digit number which are all different and can not be zero,and have to make as many 2 digit numbers from each one of them. They all give me 6 different 2 digit numbers.
What pattern will this follow in general? And what will the sums of the 2 digit numbers have in common?

I hope you can help me, thank you very much
Regards
Stef
 
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If I understood your question you are referring to http://en.m.wikipedia.org/wiki/Permutation?wasRedirected=true" of n objects, given by the factorial n!=n*(n-1)*...*1.

However how do you want to count the 2-digit numbers extracted from the 3-digit 111? Would you still count 6 or just 1?

You have to clarify what do you want to know specifically for the sum of two 2-digit numbers as I didnt get your point.
 
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Suppose you have n digits and you are extracting r (=2 in your case) digits. Then nPr is the number of ways to get a r digited no.(since, all digits are different and nonzero). Then maximum of nCr different sums will be there and r! of the numbers will have a particular sum.
 
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