An algorithm that assigns unique (values) hashes to all dates in an year.

reducedDateRepresentation.py

import time, json

big = ["January", "March", "May", "July", "August", "October", "December"]
small = ["April", "June", "September", "November"]


class DateHasher(object):
	""" duh... """
	def __init__(self, dayMultiplier=12, monthMultiplier=31):
		self.dayMultiplier = dayMultiplier
		self.monthMultiplier = monthMultiplier
		return
	def calcHash(self, dayNum, monthNum):
		dateHash = self.monthMultiplier*monthNum + self.dayMultiplier*dayNum
		return dateHash

def numOfDaysIn(monthName):
	if monthName in big:
		return 31
	elif monthName == "February":
		return 29
	else:
		return 30

def shortcutDo():
	hashes = list()
	months = big+small+["February"]
	getDateHash = DateHasher().calcHash
	for aMonth in months:
		monthNum = time.strptime(aMonth, "%B").tm_mon
		for i in range(1, numOfDaysIn(aMonth)+1):
			hashes.append(
				getDateHash(i, monthNum)
			)
	return len(set(hashes))

	# dateHash = 29*m + 12*d
	# dateHash = 17*m + 57*d
	# not working
	# dateHash = 3*m + 2*d
	# dateHash = 29*m + 11*d
	# dateHash = 3*m + 12*d
def do():
	hashes = dict()
	getDateHash = DateHasher().calcHash
	months = big+small+["February"]
	for aMonth in months:
		monthNum = time.strptime(aMonth, "%B").tm_mon
		for i in range(1, numOfDaysIn(aMonth)+1):
			dh = getDateHash(i, monthNum)
			if dh in hashes.keys():
				raise ValueError("\n\n\tHash Collision at: {}, {}".format(aMonth, i))
			else:
				hashes[dh] = "%(aMonth)s, %(i)d" % locals()
	# # February
	# for i in range(1, 29+1):
	# 	dh = getDateHash(dayNum=i, monthNum=2)
	# 	if dh in hashes.keys():
	# 		raise ValueError("\n\n\tHash Collision at: February, "+str(dayNum))
	# 	else:
	# 		hashes[dh] = "February, %(i)d" % locals()
	# # 31 day months
	# for aMonth in big:
	# 	monthNum = time.strptime(aMonth, "%B").tm_mon
	# 	for i in range(1, 31+1):
	# 		dh = getDateHash(i, monthNum)
	# 		if dh in hashes.keys():
	# 			raise ValueError("\n\n\tHash Collision at: {}, {}".format(aMonth, i))
	# 		else:
	# 			hashes[dh] = "%(aMonth)s, %(i)d" % locals()
	# # 30 day months
	# for aMonth in small:
	# 	monthNum = time.strptime(aMonth, "%B").tm_mon
	# 	for i in range(1, 30+1):
	# 		dh = getDateHash(i, monthNum)
	# 		if dh in hashes.keys():
	# 			raise ValueError("\n\n\tHash Collision at: {}, {}".format(aMonth, i))
	# 		else:
	# 			hashes[dh] = "%(aMonth)s, %(i)d" % locals()
	return hashes

def main():
	print(shortcutDo())
	# return
	ans = do()
	# print(len(ans))
	print(json.dumps(ans, sort_keys=True, indent=4))
	return

if __name__ == '__main__':
	main()