Presa una data del tipo:

${\displaystyle gg/mm/ssaa\,\!}$

una formula matematica che permette di conoscere il giorno della settimana è la seguente:

${\displaystyle Gs=\left(S+A+M+G-2^{X}\,\!\right){\bmod {7}}}$

dove

${\displaystyle S=\left[2\times \left(4-ss\ {\bmod {4}}\right)\right]{\bmod {7}}}$

${\displaystyle A=\left[\left(aa\ {\bmod {2}}8\right){\bmod {4}}+5\times \left({\mathcal {b}}{\frac {aa\ {\bmod {2}}8}{4}}{\mathcal {c}}\right)\right]{\bmod {7}}}$

${\displaystyle M=\left[3\times {\mathcal {b}}\left({\frac {mm}{2}}+{\mathcal {b}}{\frac {mm}{9}}{\mathcal {c}}\times {\frac {1}{2}}\right){\mathcal {c}}+2\times \left({\mathcal {b}}{\frac {mm}{5}}{\mathcal {c}}+{\mathcal {b}}{\frac {mm}{7}}{\mathcal {c}}+{\mathcal {b}}{\frac {mm}{12}}{\mathcal {c}}\right)\right]{\bmod {7}}}$

${\displaystyle G=gg\ {\bmod {7}}}$

Errore del parser (funzione sconosciuta '\begin{cases}'): {\displaystyle X = \begin{cases}0, & mm > 3\quad o \quad aa \bmod4 ≠ 0 \quad o \quad (S ≠ 1 e aa = 0) \\ 1, & altrimenti \end{cases}}

Gs indica il giorno della settimana (0 = sabato, 1 = domenica, 2 = lunedì..).

Data: 27/11/1989

S = 2

 ${\displaystyle S=\left[2\times \left(4-19\ {\bmod {4}}\right)\right]{\bmod {7}}}$
   ${\displaystyle =\left[2\times \left(4-3\right)\right]{\bmod {7}}=2{\bmod {7}}=2}$

A = 6

 ${\displaystyle A=\left[\left(89\ {\bmod {2}}8\right){\bmod {4}}+5\times \left({\mathcal {b}}{\frac {89\ {\bmod {2}}8}{4}}{\mathcal {c}}\right)\right]{\bmod {7}}}$
   ${\displaystyle =\left[5{\bmod {4}}+5\times \left({\mathcal {b}}{\frac {5}{4}}{\mathcal {c}}\right)\right]{\bmod {7}}=\left[1+5\times 1\right]{\bmod {7}}=6{\bmod {7}}=6}$

M = 3

 ${\displaystyle M=\left[3\times {\mathcal {b}}\left({\frac {11}{2}}+{\mathcal {b}}{\frac {11}{9}}{\mathcal {c}}\times {\frac {1}{2}}\right){\mathcal {c}}+2\times \left({\mathcal {b}}{\frac {11}{5}}{\mathcal {c}}+{\mathcal {b}}{\frac {11}{7}}{\mathcal {c}}+{\mathcal {b}}{\frac {11}{12}}{\mathcal {c}}\right)\right]{\bmod {7}}}$ 
   ${\displaystyle =\left[3\times {\mathcal {b}}\left({\frac {11}{2}}+1\times {\frac {1}{2}}\right){\mathcal {c}}+2\times \left(2+1+0\right)\right]{\bmod {7}}=\left[3\times {\mathcal {b}}6{\mathcal {c}}+2\times 3\right]{\bmod {7}}=\left(18+6\right){\bmod {7}}=24{\bmod {7}}=3}$

G = 6

 ${\displaystyle G=27\ {\bmod {7}}=6\,\!}$

X = 0

Giorno della settimana : Lunedì (2)

 ${\displaystyle Gs=\left(S+A+M+G-2^{X}\,\!\right){\bmod {7}}}$
 ${\displaystyle =\left(2+6+3+6-2^{0}\,\!\right){\bmod {7}}=\left(17-1\,\!\right){\bmod {7}}=16{\bmod {7}}=2}$

Data 15/2/14