What day of the week was 1st January 2400 (a leap century year)?

hard Q10 of 15

Reasoning Ability - Calendar Problems

ASaturday

BFriday

CWednesday

DThursday

Step-by-Step Solution

Step 1: Adjust month and year for Zeller
Since January is treated as month 13 of the previous year, use q = 1, m = 13, year = 2399.
Step 2: Compute K and J
K = 2399 % 100 = 99, J = floor(2399 / 100) = 23.
Step 3: Evaluate Zeller’s components
floor(13*(13+1)/5) = 36;
floor(K/4)=24;
floor(J/4)=5;
5*J = 115.
Total = h = (1 + 36 + 99 + 24 + 5 + 115) = 280 → 280 mod 7 = 0.
Step 4: Map result to weekday
Zeller mapping: 0 = Saturday, 1 = Sunday, 2 = Monday, 3 = Tuesday, 4 = Wednesday, 5 = Thursday, 6 = Friday. So h = 0 → Saturday.
Final Answer:
Saturday → Option A
Quick Check:
Since 2400 is divisible by 400, it’s a leap century. Verified with proleptic-Gregorian data → 1-Jan-2400 = Saturday ✅

Quick Trick: For January and February, use the previous year in Zeller’s formula. Century years divisible by 400 remain leap years.

Common Mistakes:

MISTAKES

Assuming 2400 behaves like 2100 or 2200 (non-leap) — it’s leap since divisible by 400.

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