1 Jan 1901 = (1900 years + 1^st Jan 1901)

We know that number of odd days in 400 years = 0

Hence the number of odd days in 1600 years = 0 [Since 1600 is a perfect multiple of 400]

Number of odd days in the period 1601-1900

= Number of odd days in 300 years

= 5 x 3 = 15 = 1

[As we can reduce perfect multiples of 7 from odd days without affecting anything]

1^st Jan 1901 = 1 odd day

Total number of odd days = (0 + 1 + 1) = 2

2 odd days = Tuesday

Hence 1 January 1901 is Tuesday.