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Number Theory and Combinatorics

In: Mathematical Olympiad Challenges

Author

Listed:
  • Titu Andreescu

    (University of Nebraska, American Mathematics Competitions)

  • Răzvan Gelca

    (University of Michigan, Department of Mathematics)

Abstract

1. Let a,b,c,d,e,f be the six digits of the number, arranged in increasing order of their valaue. Choose for the first three digits f,c,aand for the last three digits e,d,b. Then f+c+a−e−d−b = (f−e)+(c−d)+(a−b) ≤ f−e≤9, since c−d and a−b are negative or zero. Also, e+d+b−c−a = (e−f)+(b−c)+(d−a)≤d−a≤9. Hence the number fcaedb satisfies the desired property.

Suggested Citation

  • Titu Andreescu & Răzvan Gelca, 2000. "Number Theory and Combinatorics," Springer Books, in: Mathematical Olympiad Challenges, chapter 0, pages 197-249, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2138-8_6
    DOI: 10.1007/978-1-4612-2138-8_6
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