The mishkan and the fencepost problem

Question

Rashi (Shemos 26:6, 26) counts out the number of poles for the chatzer (courtyard of the Tabernacle) on each side in parshas Terumah. He seems to ignore what is called the Fencepost Problem. The same problem exists for the 20 amah enclosure on the East side. Do any of the commentators address this?

Answer 1

If I understand correctly, you are referring to the brichim, the horizontal poles that were slipped through rings on the boards -- and through holes within the boards -- to hold them in place. The math is straightforward: There were 20 boards of 1.5 amos on the north and south, thus requiring the poles to span 30 amos (the top and bottom poles were 2 x 15 amos, and the middle pole 1 x 30 amos). On the west was 8 boards of 1.5 amos, which required the poles to span 12 amos (again, top and bottom 2 x 6, middle 1 x 12).

Now, the 8 boards on the west overlapped one amah of the ones on the north and south. But evidently the poles on the N and S sides did not extend over the thickness of the western boards. So the math works out perfectly.

Answer 2

As far as I understand, Rashi only says that there was a 5 amos span in between amudim in reference to the possuk discussing southern wall. He also explains that the south-eastern corner post was of the southern count and the 3 of the southern Shoulder are 15 amos towards the center and the same is mirrored on the northern side. The question remains for the west wall. The possuk says there were 10 amudim so there must have been a different span, namely 50/9 amos. The east gate masach must also have different spans. 20/3 = 6 2/3 amos because there were 4 amudim so three spans and 20 amos.

Ikur Sifsei chachamim assumes universal span and lays out in clockwise direction the next sides first amud holding up the end of each side and ends up attributing this to rashi which doesn't work with rashi's explanation of the shoulders.

Answer 3

This is a question that has bothered people for a long time. Part of the problem is that even if you were to come up with an ingenious answer, it still wouldn't explain why Rashi seems to have left out whatever idea you came up with.

Now, to lay out the problem fully: The verses refer to a side as a peiah/פאה. Rashi to Exodus 27:9 defines that as the entire side. So you can't say that the poles in the northwest and southwest corner did double-duty for both sides, in order to gain another space on the north and south sides, because then there would be twenty-one poles to a side.

If you read the verses there carefully, you'll see that when describing the north and south side, the verse uses the singular "its poles", and when describing the west side, the verse uses the plural "their poles". The antecedent of the singular it would be the side/peiah, and the antecedent of the plural their would be the fifty amos of the west side.

(ט) {שביעי} וְעָשִׂ֕יתָ אֵ֖ת חֲצַ֣ר הַמִּשְׁכָּ֑ן לִפְאַ֣ת נֶֽגֶב־תֵּ֠ימָ֠נָה קְלָעִ֨ים לֶחָצֵ֜ר שֵׁ֣שׁ מׇשְׁזָ֗ר מֵאָ֤ה בָֽאַמָּה֙ אֹ֔רֶךְ לַפֵּאָ֖ה הָאֶחָֽת׃ (י) וְעַמֻּדָ֣יו עֶשְׂרִ֔ים וְאַדְנֵיהֶ֥ם עֶשְׂרִ֖ים נְחֹ֑שֶׁת וָוֵ֧י הָעַמֻּדִ֛ים וַחֲשֻׁקֵיהֶ֖ם כָּֽסֶף׃ (יא) וְכֵ֨ן לִפְאַ֤ת צָפוֹן֙ בָּאֹ֔רֶךְ קְלָעִ֖ים מֵ֣אָה אֹ֑רֶךְ וְעַמֻּדָ֣ו עֶשְׂרִ֗ים וְאַדְנֵיהֶ֤ם עֶשְׂרִים֙ נְחֹ֔שֶׁת וָוֵ֧י הָֽעַמֻּדִ֛ים וַחֲשֻׁקֵיהֶ֖ם כָּֽסֶף׃ (יב) וְרֹ֤חַב הֶֽחָצֵר֙ לִפְאַת־יָ֔ם קְלָעִ֖ים חֲמִשִּׁ֣ים אַמָּ֑ה עַמֻּדֵיהֶ֣ם עֲשָׂרָ֔ה וְאַדְנֵיהֶ֖ם עֲשָׂרָֽה׃ (יג) וְרֹ֣חַב הֶֽחָצֵ֗ר לִפְאַ֛ת קֵ֥דְמָה מִזְרָ֖חָה חֲמִשִּׁ֥ים אַמָּֽה׃ (יד) וַחֲמֵ֨שׁ עֶשְׂרֵ֥ה אַמָּ֛ה קְלָעִ֖ים לַכָּתֵ֑ף עַמֻּדֵיהֶ֣ם שְׁלֹשָׁ֔ה וְאַדְנֵיהֶ֖ם שְׁלֹשָֽׁה׃ (טו) וְלַכָּתֵף֙ הַשֵּׁנִ֔ית חֲמֵ֥שׁ עֶשְׂרֵ֖ה קְלָעִ֑ים עַמֻּדֵיהֶ֣ם שְׁלֹשָׁ֔ה וְאַדְנֵיהֶ֖ם שְׁלֹשָֽׁה׃ (טז) וּלְשַׁ֨עַר הֶֽחָצֵ֜ר מָסָ֣ךְ׀ עֶשְׂרִ֣ים אַמָּ֗ה תְּכֵ֨לֶת וְאַרְגָּמָ֜ן וְתוֹלַ֧עַת שָׁנִ֛י וְשֵׁ֥שׁ מׇשְׁזָ֖ר מַעֲשֵׂ֣ה רֹקֵ֑ם עַמֻּֽדֵיהֶם֙ אַרְבָּעָ֔ה וְאַדְנֵיהֶ֖ם אַרְבָּעָֽה׃ 9) You shall make the courtyard of the Tabernacle; on the southern side, southwards there shall be hangings for the courtyard, of twined linen, one hundred cubits in length for the one side. (10) And its pillars shall be twenty, and their sockets twenty, of copper; the hooks of the pillars and their bands12 shall be of silver. (11) And so for the northern side, length-wise, there shall be hangings of one hundred cubits in length, and its pillars twenty, and their sockets twenty, of copper; the hooks of the pillars and their bands shall be of silver. (12) And for the width of the courtyard to the western side, there shall be hangings of fifty cubits, their pillars ten and their sockets ten.

So there were twenty poles each on the north and south sides, which Rashi defines as the entire side. There were ten poles for the curtains of the west side, but there were not ten poles to the west side itself, because together with the end-poles of the north and south sides, the west side had twelve poles. In other words, the poles in the northwest and southwest corners were attributed to the north and south, not the west.

So with only twenty poles, you have nineteen spaces, which should come out to about five and a quarter amos to each space. So how could Rashi possibly say there were five amos?

I believe the simple answer is that when Rashi says there was a pole every five amos, he means approximately every five amos. On the north and south side the space would have been a little more to distribute the five amos over nineteen spaces. On the west side, the space would have been a little less to distribute fifty amos over eleven spaces. On the west side, it is exactly five amos per space (15 amos for three spaces), using the end posts of the north and south sides respectively.

Answer 4

Another possible answer is that in between each 5 amos span the amud itself took up space along which there was that much kela. Nine spans on the West and 19 spans on the North and South. Two posts in western corners. The shoulders' 5 includes the amud and the masach is back to a weird span or outsized amudim.

Another possible answer which doesn't fit with Rashi's expalanation of the corner amud is that each amud held the kela from the middle by suspending the kela on a roll from cords. the 5 amos span is still produced. Exactly how this was set up is not clear.