If the third day after tomorrow is Friday, then the third day before yesterday…

Concept: For "X days after" a reference day, add X to its day index; for "X days before", subtract X. Because the week repeats every 7 days, only the net offset modulo 7 matters when relating two named days.

1. Let today be T. Then tomorrow is T + 1.

2. The third day after tomorrow is (T + 1) + 3 = T + 4. This is given as Friday, so T + 4 = Friday.

3. Counting back four days from Friday (Thursday, Wednesday, Tuesday, Monday) gives T = Monday, so today is Monday.

4. Yesterday is T − 1 = Monday − 1 = Sunday.

5. The third day before yesterday is (T − 1) − 3 = T − 4 = Sunday − 3. Counting back three days from Sunday (Saturday, Friday, Thursday) gives Thursday.

Cross-check: The gap between "the third day after tomorrow" (T + 4) and "the third day before yesterday" (T − 4) is always 8 days, i.e. one day beyond a full week (8 mod 7 = 1). So the required day is exactly one day before the given Friday, which is Thursday — confirming the step-by-step result.

So the third day before yesterday was Thursday.