The last day of a century cannot be:

Tuesday

⇒ 100 years contain 5 odd days.

∴ last day of 1st century is 'Friday'

⇒ 200 years contain (5×2)=10 odd days = 3 odd days.

 ∴ last day of 2nd century is 'Wednesday'.

⇒ 300 years contain (5×3)=15 odd days =1 odd day.

∴ Last day of 3rd century is 'Monday'.

⇒ 400 years contain 0 odd days.

∴ Last day of 4th century is 'Sunday'

Since the order is continually kept in successive cycles, we see that the last day of a century cannot be Tuesday, Thursday or Saturday.

Code List:

Day code:

Sunday        : 00

Monday        : 01

Tuesday       : 02

Wednesday : 03

Thursday     : 04

Friday          : 05

Saturday     : 06

Century Code:

Century year- 100 : 5

Century year- 200 : 3

Century year- 300 : 1

Century year- 400 : 0...