Monthly Archives: February 2015

Num3er 729243027001

       is a 12-digit perfect cube. with a digit sum of 37: and it can be sectioned in powers of 3 : since   Is a number with such properties unique?   Paul found:         … Continue reading

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Triangle | Trig questions

  Consider the triangle shown below with angles A, B, and C. Suppose that the length of the side opposite angle A has length a, the side opposite angle B has length b, and the side opposite angle C has … Continue reading

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Squares transformed into another square if a digit is increased by 1, another decreased by 1

                                           

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Squares that can be transformed into a cube if THREE digits are increased by one

                                           

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Squares that can be transformed into a cube if two digits are increased by one

    excluding   ,   ,   etc.    excluding   ,     etc        Contributor:   pipo                        

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Squares that can be transformed into another square if two digits are increased by 1

                                         

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Squares that can be transformed into a cube if one digit is increased by 1

    Paul found: 39204   =   198^2 39304   =   34^3 39204000000   =   198000^2 39304000000   =   3400^3 98831640625   =   314375^2 98931640625   =   4625^3     pipo found: 1199462890625   … Continue reading

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Are there any positive integers n such that the expansion of 2^n ends in n?

    n = 36   is the first from this list.   Any others?   @chappulian found   n = 736   and   n = 8736   @shahlock:   n = 48736 Dave Radcliffe: a(2) = 36,   … Continue reading

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Squares that can be transformed into another square if some digits are increased by 1

  Here are a few examples,   8-digit square that can be transformed into another square if the 2nd digit from the left is increased by 1. 38564100   =   39564100   =   24502500   =   25502500 … Continue reading

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Determinant | (A,B,C) are the angles in a triangle

    If   A,   B,   C   are the angles of a triangle show that                            

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