There are 2 obvious mathematical flaws. If Rosh Chodesh Elul to Rosh Hashanah is 30 days than Rosh Chodesh Elul to Yom Kippur is only 39 days (and to Shmini Atzeres is 51 days). Also since the length of Marcheshvan is not fixed the length of time between Rosh Chodesh and the last day of Chanukah is not always the same.
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