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**Soroban** Hello, mathwizard!

"If the day after tomorrow is yesterday, then today is Sunday."

. . . . . $\displaystyle _{\downarrow} \qquad \leftarrow \qquad \leftarrow \qquad \leftarrow \qquad\leftarrow\qquad \leftarrow \qquad _{\uparrow} $

. . $\displaystyle \boxed{\text{yesterday}} \quad \boxed{\text{today}} \quad \boxed{\text{tomorrow}} \quad \boxed{\text{day after tomorrow}}$

. . . . . . . . . . $\displaystyle ^{\text{Sunday}}$

We can see that everything is "set back" three days.

To restore it, everything is "set ahead" three days.

. . Hence, today is: .$\displaystyle \text{Sunday}+3\quad\rightarrow\quad\boxed{\text{ Wednesday}}$

"If the day before yesterday is the day after tomorrow..."

. . . . . . . . . . $\displaystyle _{\uparrow}\qquad \rightarrow \qquad\rightarrow\qquad\rightarrow\qquad\rightarro w \qquad\rightarrow \qquad\rightarrow\qquad\rightarrow\qquad_{\downarr ow}$

. . $\displaystyle \boxed{\text{day before yesterday}} \quad \boxed{\text{yesterday}} \quad \boxed{\text{today}} \quad \boxed{\text{tomorrow}} \quad \boxed{\text{day after tomrrow}}$

. . . . . . . . . . . . . . . . . . . . . . . .$\displaystyle ^{\text{Wednesday}}$

We see that everything is "moved ahead" four days.

Therefore, today is: .$\displaystyle \text{Wednesday}+4\quad\rightarrow\quad\boxed{\tex t{Sunday}}$