Before us is Mishnah 6 of the third chapter of Maseches Menachos. This Mishnah takes us away from the subject of menachos: since the previous Mishnah dealt with components of a minchah that are indispensable to one another, the Tanna now turns - for several Mishnayos - to additional mitzvos in matters of kodashim and beyond. Our Mishnah lists fifteen cases in which two components of a mitzvah are bound up with one another, to the point that in the absence of one the other does not count as fulfillment at all: all or nothing.
The fifteen things that are indispensable to one another:
"Shnei se'irei Yom HaKippurim" - on Yom Kippur two goats are brought: one is offered as a korban to Hashem, and the second is the goat that is sent away, the goat to Azazel that is pushed off the cliff in the Judean desert. One cannot be performed without the other, and each is indispensable to the other.
"Shnei kivsei Atzeres" - on Shavuos two lambs are brought as special korbanos, and they are waved together with the two loaves. Both are required, and one lamb alone is no better than nothing.
"Shtei challos" - the two loaves that are waved with the lambs of Shavuos. Both are required, and one without the other is meaningless.
"Shnei sedarim" - the two arrangements of the lechem hapanim. On the table in the Kodesh lie the twelve loaves of the lechem hapanim, arranged in two rows of six. Although each arrangement has a significance of its own, one without the other is nothing. And all the more so, says the Tanna, a single loaf is indispensable to the rest: one complete arrangement does not suffice, rather all twelve loaves are required.
"Shnei bezichin" - the two spoons of levonah placed upon the lechem hapanim. Both are required, and one alone is as though nothing.
"HaSedarim vehabezichin" - the two arrangements alone do not suffice; the two bezichin are required as well. Levonah without loaves, or loaves without levonah - there is no proper fulfillment of the mitzvah of lechem hapanim here.
"Shnei minim shebanazir" - a nazir who completes his nezirus brings korbanos, and with them two types of menachos: challos and rekikim, ten loaves. Challos alone or rekikim alone do not suffice, and there is no fulfillment of the mitzvah of the bread at all.
"Sheloshah shebaparah" - the three components thrown into the fire of the parah adumah. In preparing the mei chatas, the purifying waters made from the ashes of the parah, the red heifer is burned on Har HaZeisim, and three components are added into the fire: cedar wood, eizov (hyssop), and shni tola'as - wool dyed red. If all of them, or even one of them, is missing, there is nothing.
"Arba'ah shebatodah" - the four kinds of bread that accompany the korban todah. The todah is a sacrifice in its own right, a form of shelamim, and it is accompanied by forty loaves - ten of each of the four kinds, and one of each kind is given to the kohen. The four kinds are: challos, rekikim (baked in an oven, like those of the nazir), soles murbeches, and chametz bread - leavened loaves that are not offered on the mizbe'ach but are eaten. Three kinds alone are of no avail. We will learn more about this, with Hashem's help, later in the maseches.
"Arba'ah shebalulav" - the four species taken on Sukkos. All four are required: without an esrog there is no benefit in taking the lulav, and likewise the reverse. The intent is not to require binding them together, for the Tannaim disagreed as to whether a lulav requires an agud, and the halachah is that it does not require an agud - one who takes the lulav and shakes it, and afterward the esrog, the hadassim and the aravos separately, has fulfilled his obligation. And the custom to bind them and shake them all as one is only on account of "zeh Keli ve'anveihu", to beautify the mitzvah. The novelty of the Mishnah is that even with separate takings, if one of the species is missing - for example, he has no esrog and cannot obtain one that day - there is no benefit in shaking the other three, for three are as though nothing. However, in halachah, one who does not know whether he will obtain all four species does not recite a berachah; but if he estimates that he will obtain them, he takes and shakes what he has now, and the rest during the course of the day, in order to shake all four species.
"Arba'ah shebametzora" - the four components in the process of the metzora's purification. The beginning of the process: two birds are taken, one is slaughtered and its blood drips into an earthenware vessel containing living water from a spring. Afterward, four components are dipped into those waters: the second bird - the living bird - and alongside it cedar wood, eizov and shni tola'as (the red thread) bound together. With all four, the water into which the blood dripped is sprinkled upon the metzora, and if one of them is missing the act is ineffective.
"Sheva hazaos shebaparah" - as part of the service of the parah adumah and the preparation of the mei chatas, the kohen sprinkles on Har HaZeisim - the mountain lying just to the east of Har HaMoriah, on which Har HaBayis stands - seven sprinklings of blood in the direction of the Kodesh HaKodashim, toward which he aims. Even though he is far from the Beis HaMikdash, he must aim toward that side, and if he did not perform all seven sprinklings, it is indispensable.
The last three cases - the sprinklings of the blood:
The last three cases are interwoven with one another, and therefore will be explained as a single unit: "Sheva hazaos shebein habadim" - the sprinklings performed in the Kodesh HaKodashim between the staves of the Aron; "veshel haparoches" - the sprinklings upon the paroches or opposite it, the curtain separating the Kodesh from the Kodesh HaKodashim; "veshel mizbach hazahav" - the sprinklings given upon the golden mizbe'ach. All of them are indispensable to one another, and if a single sprinkling of blood is missing there is nothing.
These cases relate to the five inner chataos: five chatas offerings whose blood is offered within, in the Heichal, meaning that the blood is placed in various locations within the Heichal and not upon the outer mizbe'ach. These five korbanos have special laws, and they can be divided into two groups.
Two of them are the two chataos of Yom Kippur: the goat offered to Hashem, and the bull of the Kohen Gadol brought on behalf of the kohanim and their households. In these two korbanos, forty-three sprinklings of blood are given.
The order of the matter: the blood of each of the two is placed once upward and seven times downward - eight times - between the staves, inside the Kodesh HaKodashim before the Aron, and for both korbanos together, sixteen sprinklings. Afterward the blood is placed before the separating paroches, again once upward and seven downward, eight for each and sixteen for the two - thus thirty-two. At this stage the blood of the two is mixed, and eleven further placements are given: seven upon the top of the golden mizbe'ach, the inner mizbe'ach in the Kodesh, and four upon its four corners. Eleven and thirty-two - forty-three sprinklings. The novelty of our Mishnah is that all of them are indispensable to one another, and if only forty-two were performed and one of them is missing, the obligation has not been fulfilled.
The other three inner chataos are:
Par he'elem davar shel tzibbur - a korban brought by the community when the Sanhedrin ruled leniently regarding a prohibition carrying kares, and afterward retracted and it became clear that they had erred. If the majority of the community followed their ruling, this bull is brought on behalf of them all in place of individual chataos.
Par kohen mashiach - a similar situation, except that here the Kohen Gadol ruled for himself - and not the Sanhedrin for the community - and was lenient regarding a prohibition carrying kares, and in the end it became clear that he had erred.
Se'ir chatas of avodah zarah - when the Sanhedrin's lenient ruling regarding a prohibition carrying kares concerned avodah zarah, a goat is brought instead of the par he'elem davar.
In these three as well there are placements of blood, but far fewer: they include no placements in the Kodesh HaKodashim at all, but rather seven opposite the paroches and four upon the four corners of the mizbe'ach, eleven in all, and no more - not upon the top of the mizbe'ach and not in the Kodesh HaKodashim. And all eleven of these, just like the sprinklings enumerated above, are indispensable to one another: if one of them is missing the entire service is invalid, and everything must be done anew.
In summary: in this Mishnah we enumerated fifteen things that are indispensable to one another - from the two goats of Yom Kippur and the two lambs of Shavuos, through the two loaves, the arrangements of the lechem hapanim and the bezichin, the kinds brought by the nazir, the components of the parah adumah, the kinds of the todah, the four species and the components of the metzora's purification, and up to the sprinklings of blood of the parah and of the five inner chataos. In all of them there is one principle: the components are bound up with one another, and if one of them is missing the rest do not count as fulfillment at all.