The following are obligated in challah but exempt from tithes: gleanings, forgotten sheaf, pe'ah, ownerless produce, maaser rishon from which terumah was removed, maaser sheni and consecrated produce that were redeemed, the surplus of the Omer, and grain that has not yet reached one-third ripeness. R' Eliezer says: grain that has not reached one-third ripeness is also exempt from challah.
Fuchsia — Rule
Gold — Name of Tana
Black — Case
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The surplus of the Omer — what happens to the leftover flour
3 se'ah raw barley
שָׁלשׁ סְאִין
The starting quantity for the Omer
→
1 isaron set aside
עִשָּׂרוֹן
The Omer offering brought to the altar
→
~9 isarons surplus
מוֹתַר הָעֹמֶר
Redeemed from the Beis HaMikdash into the market
Note on the seah measure: Many meforshim understand the 3 se'ah (or 5 se'ah on a weekday, per R' Yishmael in Menachos 10:1) not as the raw quantity of barley harvested, but as the amount of flour the barley must be sufficient to yield. On this reading, 3 se'ah of flour = 10 isarons; after separating 1 isaron for the Omer itself, approximately 9 isarons of flour constitute the surplus (מוֹתַר הָעֹמֶר) that is redeemed and enters the market.
Why challah yes, tithes no — the legal mechanism
Challah — obligated
חַיָּב בַּחַלָּה
Challah attaches at the moment of kneading. The surplus is redeemed and enters private hands before kneading — at that point challah applies, just like any other privately owned dough from these five grains.
Tithes — exempt
פָּטוּר מִן הַמַּעַשְׂרוֹת
Tithes attach at the moment of miru'ach (smoothing the grain pile). At the time of miru'ach, the grain was still Temple property — therefore exempt from tithes. The tithe window has already closed before the grain enters private hands.
The full list — grain obligated in challah but exempt from tithes
These all share one feature: they were communal or Temple property at the time tithes normally attach
לֶקֶט, שִׁכְחָה, פֵּאָה
Gleanings, forgotten sheaf, pe'ah — given to the poor; tithes already exempted
הֶפְקֵר
Ownerless produce — no owner at the time tithes attach
מַעֲשֵׂר רִאשׁוֹן שֶׁנִּטְּלָה תְרוּמָתוֹ
First tithe after terumah removed — already processed through the tithe system
מַעֲשֵׂר שֵׁנִי וְהֶקְדֵּשׁ שֶׁנִּפְדּוּ
Redeemed second tithe and sanctified produce — tithe already separated previously
מוֹתַר הָעֹמֶר
Surplus of the Omer — Temple property at miru'ach; redeemed into the private market from the Beis HaMikdash; challah attaches only later at kneading.
תְּבוּאָה שֶׁלֹּא הֵבִיאָה שְׁלִישׁ
Under-one-third ripe grain — R' Eliezer exempts even from challah; Chachamim oblige
Position in the Omer to Shavuos arc — 43 mishnayos
Preceding · Mishnah 14
Menachos 10:4
The processing — including extraction of the isaron and redemption of the surplus
Current · Mishnah 15
Challah 1:3 — What Happens to the Surplus
Movement II·C opens
Mishnah 14 ended with "the surplus is redeemed and eaten by anyone." This mishnah answers: what is its legal status? Challah yes, tithes no. The mechanism is precise: at the moment tithes normally attach (miru'ach), the grain was still Temple property — exempt. But when the surplus is redeemed from the Beis HaMikdash and enters private hands, challah attaches at kneading. A practical halacha with an Omer connection.
Following · Mishnah 16
Menachos 5:3
The Omer's oil and frankincense — comparing to the Shtei HaLechem