23rd January is the birthday of Netaji Subhas Chandra Bose, 30th January is Martyr’s Day, 1st May is the World Labourer’s Day, 2nd October is the birthday of Mahatma Gandhi and 25th December is Christmas. In every year (not a leap year), they will fall on the same day as the difference between any two of them is always a multiple of ‘7’, the number of days in a week. It is easy to see that between the given five days these are progressively 7, 91, 154 and 84.
One interesting implication – if one of them is a Sunday, then each is a Sunday as it happened in 2011. Each of them except 30 January is a holiday in West Bengal every year. Hence, the people of that state did not get the benefit of four holidays in 2011. It would happen again in 2022.