( 0 ! + 0 ! + 0 ! ) ! = 6 {\displaystyle (0!+0!+0!)!=6}
( 1 + 1 + 1 ) ! = 6 {\displaystyle (1+1+1)!=6}
2 + 2 + 2 = 6 {\displaystyle 2+2+2=6}
2 ⋅ 2 + 2 = 6 {\displaystyle 2\cdot 2+2=6}
( 2 ⋅ 2 2 ) = 6 {\displaystyle {\binom {2\cdot 2}{2}}=6}
3 ! 3 3 = 6 {\displaystyle 3!{3 \over 3}=6}
( 3 3 3 ) ! = 6 {\displaystyle ({\sqrt[{3}]{3^{3}}})!=6}
4 + 4 + 4 = 6 {\displaystyle {\sqrt {4}}+{\sqrt {4}}+{\sqrt {4}}=6}
4 ! 4 ⋅ 4 = 6 {\displaystyle {{4!} \over {\sqrt {4\cdot 4}}}=6}
5 + 5 5 = 6 {\displaystyle 5+{5 \over 5}=6}
6 6 6 = 6 {\displaystyle 6{6 \over 6}=6}
6 6 6 = 6 {\displaystyle {\sqrt[{6}]{6^{6}}}=6}
7 − 7 7 = 6 {\displaystyle 7-{7 \over 7}=6}
( 8 + 8 8 ) ! = 6 {\displaystyle ({\sqrt {8+{8 \over 8}}})!=6}
( 9 ) ! 9 9 = 6 {\displaystyle ({\sqrt {9}})!{9 \over 9}=6}
( log 10 + log 10 + log 10 ) ! = 6 {\displaystyle (\log 10+\log 10+\log 10)!=6}
Für den Rest aller ganzen Zahlen
| cos n π + cos n π + cos n π | ! = 6 ∀ n ∈ Z {\displaystyle \left|\cos n\pi +\cos n\pi +\cos n\pi \right|!=6~\forall ~n\in \mathbb {Z} }
( n ( n − n ) − e i π − e i π − e i π ) ! = 6 ∀ n ∈ Z {\displaystyle (n(n-n)-e^{i\pi }-e^{i\pi }-e^{i\pi })!=6~\forall ~n\in \mathbb {Z} }
![{\displaystyle ({\sqrt[{3}]{3^{3}}})!=6}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c8d4a13f3ba96f3279e515bcd80423b2be12152b)
![{\displaystyle {\sqrt[{6}]{6^{6}}}=6}](https://wikimedia.org/api/rest_v1/media/math/render/svg/406fbb8549cc0f265f1a389b57917881d2035d91)
