Monthly Archives: February 2014

Puzzle: Sum of the factorials of the digits of an Integer N

    To find integers N such that the sum of the factorials of the digits of N is equal to the reversal of its largest prime factor. In the first example, 143   =   11   X   … Continue reading

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(a/(a+b))^2 + b/(a+b) = (b/(a+b))^2 + a/(a+b)

    Can you find other examples?                  

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Right Triangles (a, √(a+c), c)

                   

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Puzzle : Acute Triangles – Area is 4 times the perimeter

  Find all the acute triangles whose sides are integers and whose area is 4 times its perimeter.                                                      ——————————————   Puzzle #1 Paul found:       Obtuse and Right triangles :                                                    ——————————————   Puzzle … Continue reading

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Positive integers (a,b,c); a^2 – a*b + b^2 = c^2

  Here are few examples:     Find more examples.        

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The sum of the first n natural numbers and other sums

    @grey_matter noticed a pattern with Pascal’s triangle                                                    ——————————————   #2                                                      ——————————————   #3                                                                    ——————————————   #4 Paul adds:           … Continue reading

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Triangle whose angles are 15, 55, 110

      How Euler Did It http://eulerarchive.maa.org/hedi/HEDI-2004-04.pdf                  

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Repunits and Repdigits | x + y^2 = z

  A repunit is a number consisting of copies of the single digit 1. repunits have the form   (10^n – 1)/9 Repunit http://mathworld.wolfram.com/Repunit.html http://en.wikipedia.org/wiki/Repunit Repdigit http://mathworld.wolfram.com/Repdigit.html http://en.wikipedia.org/wiki/Repdigit         Prove that the pattern continues.   @ChrisMaslanka solved … Continue reading

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x + x – (x+1) = x^n + x^n – (x+1)^n

           

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Four Rectangles, 2 Squares

                                      Solution: Abdul Hafiz Kaissi answered correctly        

Posted in Geometry, Math Beauty, Number Puzzles | Tagged , | 1 Comment