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

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

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

...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

...

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

Five Fives

From charlesreid1

Five Fives