# 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

Posted in Number Puzzles | Tagged , | 2 Comments

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

Can you find other examples?

Posted in Number Puzzles | | 2 Comments

## Right Triangles (a, √(a+c), c)

Posted in Geometry, Number Puzzles | Tagged | 1 Comment

## 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

Posted in Geometry, Number Puzzles | Tagged | 6 Comments

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

Here are few examples:     Find more examples.

Posted in Math Beauty, Number Puzzles | Tagged , | 3 Comments

## 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

Posted in Number Puzzles | | 4 Comments

## Triangle whose angles are 15, 55, 110

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

Posted in Geometry | Tagged , , , , | 2 Comments

## 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