purim torah in jest - How big did Mordechai get, and was it only in the king's palace?

According to the Megillah (9:4), Mordechai grew to a very large size whenever he was in the king's palace (כִּי־גָדוֹל מָרְדֳּכַי בְּבֵית הַמֶּלֶךְ ... כִּי־הָאִישׁ מָרְדֳּכַי, הוֹלֵךְ וְגָדוֹל).

How large did Mordechai grow, and did he return to normal size upon venturing outside?

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Answer

It is known that מרדכי's other name was "פתחיה". The names are related as follows: If you double the g'matriya of the first three letters of "מרדכי", you get the first three of "פתחיה"; and if you halve the last two of "מרדכי", you get the last two of "פתחיה".

• מ doubled is פ;


• ר doubled is ת;



• ד doubled is ח;


• כ halved is י;


• י halved is ה.

Continuing the trend, let's multiply the letters of "מרדכי" by other powers of two:

• מ eighthed is ה;


• ר quadrupled is תת;


• ד quartered is א;


• כ doubled is מ;



• י halved is ה.

Thus, מרדכי was ה׳תת אמה‎, 5800 amos tall. As mentioned in the pasuk, of course, this was only in the royal palace. The palace must have had very high ceilings, which is why the beginning of Ester, which describes the palace floors and other furnishings, doesn't describe the ceilings: anything more than twenty amos up is not noticed, as we see in hilchos Chanuka.