From charlesreid1

See also: Four Fours

Five Fives

Extending the idea of Four Fours, where the intention is to write each integer as a combination of 4 4's (any mathematical symbol is allowed except for digits that are not 4), we can create the game of Five Fives.

It is also useful to build a table of different combinations of 5 to help out: Five Fives/Table of 5s


1 = \left( \dfrac{  \ln{\left(\dfrac{5}{\sqrt{5}} \right) }  }{  \ln{5}   } \right) + \left(  \dfrac{  \ln{\sqrt{5}}   }{   \ln{5}   } \right)


1 = \dfrac{5 \times 5 \times 5 - 5}{5!}

...


5 = \dfrac{ \sqrt{5}^{\sqrt{5}} \sqrt{5} }{ 5 \times 5 }


6 = 5 + \dfrac{5 \times 5}{5 \times 5}


7 = 5 + \dfrac{5}{5} + \dfrac{5}{5}


8 = 5 + \dfrac{5+5+5}{5}


9 = \sqrt{5} \sqrt{5} + 5 - \dfrac{5}{5}


10 = \dfrac{5 \times 5 + 5 \times 5}{5}


11 = \dfrac{5 \times 5 + 5}{5} + 5


12 = 5 + 5 + \dfrac{5+5}{5}


13 = 5 + 5 + 5 - \dfrac{ \ln{5} }{ \ln{\sqrt{5}} }


14 = 5 + 5 + 5 - \dfrac{5}{5}


15 = \left( \dfrac{5+5}{5} \right) \times 5 + 5


16 = 5 + 5 + 5 + \dfrac{5}{5}


17 = 5 + 5 + 5 + \dfrac{ \ln{5} }{ \ln{\sqrt{5}} }


18 = 5 \times 5 - 5 - \dfrac{\ln{5}}{\ln{\sqrt{5}}}


19 = 5 \times 5 - 5 - \dfrac{5}{5}


20 = \dfrac{5}{5} \left( 5 \times 5 - 5 \right)

...


25 = \dfrac{5^5}{5} - 5 \times 5!