The Jewish Calendar and Holidays (incl. Sabbath): Other Holidays and Fasts: Chanukah Gelt:
Why do we give money to children on Chanukah?
It was customary to give coins to children to
induce them to study (Maimonides' Mishnah
commentary on Sanhedrin Ch.10). Giving coins
to children on Chanukah is therefore appropriate,
because Chanukah commemorates our victory over
the Syrians, who had forbidden the study of Torah.
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