Apologies for not posting last weekend, I was traveling on a short vacation!
This was a relatively easy puzzle, many people sent me the correct answer. Folks who sent me the correct answer include Karan Sharma, Suman Saraf, Sanjeev Dugar, Anirudh Baddepudi, Girish Tutakne, Sri Peddu, Sandeep Verma, Alok Kuchlous, Prakhar, Alankrita Agrawal, Praneeth, Chandu Karan, Pratik Poddar and Rahul Garg – Well done all!
The answer is Feb 28, 29, March 1, 2 and 3 – therefore this is possible only in a leap year.
For any five contiguous numbers, the sum is divisible by 5. Since 63 is not, it can only mean that there is a cut off at the end of the month in the sequence of 5 dates. Since all months end between 28 and 31, we can figure out by simple trial and error that there need to be two dates at the end of the month followed by 1, 2 and 3 of the following month. This implies that the two dates need to add up to 57, which again implies that the dates can only be 28th and 29th, and hence Feb 28 and 29th of a leap year.
Hope you all enjoyed the puzzle!