Multi-year weekday shift from a known Jan 1: If it was Sunday on January 1, 2006, what was the day of the week on January 2, 2010?

Introduction / Context:
Across several years, we sum yearly shifts: +1 for each common year and +2 for each leap year encountered. After reaching the target year’s same date, we add the remaining day offset to reach the exact target date.

Given Data / Assumptions:

• Jan 1, 2006 = Sunday.
• We need Jan 2, 2010.
• Year-by-year: 2006 (+1), 2007 (+1), 2008 (leap, +2), 2009 (+1).

Concept / Approach:
Compute the net shift to Jan 1, 2010, then step one more day to Jan 2, 2010.

Step-by-Step Solution:

Verification / Alternative check:
Modulo arithmetic: 365 ≡ 1, 366 ≡ 2 (mod 7); accumulated = 5; then +1 day.

Why Other Options Are Wrong:
Thursday/Sunday/Friday reflect partial steps; only Saturday matches full accumulation.

Common Pitfalls:
Forgetting to add the extra one day from Jan 1 to Jan 2 after computing the multi-year shift.

Final Answer:
Saturday