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The Gemara in Nedarim 32B states;

הַשָּׂטָן בְּחוּשְׁבָּנֵיהּ תְּלָת מְאָה וְשִׁיתִּין וְאַרְבְּעָה

The letters of the term the Satan [haSatan] in numerical value is 364, which equals the number of days of the year, except for Yom Kippur, during which he has no power.

The English Translation (from Sefaria) seems to be based on the Ran;

השטן בחושבנא תלת מאה ושיתין וארבע הוו - וימות החמה שס''ה א''כ איכא חד יומא דלית ליה רשותא למשטן דהיינו יוה''כ:

My question is that 365 days is in a solar year while Yom Kippur is based on the lunar year. This means that aside from a lunar leap year, there will be 2 Yom Kippur days within 365 days of each other. It seems incongruent to work off of the solar number for the total value and the solar calendar for the "Day off".

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  • In regards to the Ketores it says that there were 368 Portions / 365 for each sun day / 3 additional for Tom Kippur. Thus you see that there are other Jewish items that are based on the solar year. In actuality the Jewish year is interwined with the solar year and we have leap years to make this conversion accurate. At the end of the day the average Jewish lunar year is 365 days also. Commented Jul 23, 2021 at 15:22
  • The Ketores could be was only done every 365 days and/or the extra was put away as the brasia states every 60 to 70 years they used it for half. But we do see again that Yom kippur is mentioned and again the 365 days, but Yom Kippur comes every 354 days or every 384 days not 365.
    – Chatzkel
    Commented Jul 23, 2021 at 15:26
  • However in a 19 year cycle of 7 additional Adars, the Jewish year averages to 365 days per year. Commented Jul 23, 2021 at 15:27
  • But if the Solar year starts in Tishrei (October) according to R' Elazar then there would be a number of Solar years with 2 Yom Kippurs, year 1 for example would have 2 Yom Kippurs
    – Chatzkel
    Commented Jul 23, 2021 at 15:34
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    See yaros divash drush vav who answers this question. He says nun and mem are interchangable. Says kabbala stuff there which i didn't understand.
    – Shlomy
    Commented Jul 23, 2021 at 16:54

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