Prove that last day of a century cannot be Tuesday, Thursday or Saturday.
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Sol. 100years have = 5 odd days ∴ Last days of Ist century is Friday
200years have = 10 odd days ∴ Last day of IIst century is Wednesday
= 3 odd days
300years have = 15 odd days ∴ Last day of IIIrd century is Monday
= 01 odd day
400years have = (5 × 4 + 1) Last day of 4th century is Sunday
= 21 odd days
= 0 odd days
Since the order keeps on cycling, we see that the lat day of the century cannot be Tuesday, Thursday or Saturday.
| Tables: For calculating odd days | ||||||||||||
| Month | Jan | Feb | March | April | May | June | July | Aug | Sep | Oct | Nov | Dec |
| Odd days | 3 | 0/1 ord./Leap yr | 3 | 2 | 3 | 2 | 3 | 3 | 2 | 3 | 2 | 3 |
| Months of years | Ist three months 1 Jan to 31 March | IInd Three months 1 Apr to 30 Jun | IIIrd three months 1 July to 30 Sep. | Ivth (last) three months | Total year 1 Jan to 31 Dec. |
| Total days | 90 / 91 ord / leap | 91 | 92 | 92 | 365/366 ord./leap |
| Odd days | 6 / 0 ord./leap | 0 odd day | 1 odd day | 1 odd day | 1 / 2 odd days |
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