Gemara

Ula visited the house of Rav Menasheh; a man banged on the door.

Ula: Who is desecrating Shabbos [through producing sounds]?

Rabah (some texts - Rava): (It is permitted.) Chachamim forbade only musical sounds.

Question: Rav Yehudah forbids women to play with nuts (roll them on boards) on Shabbos;

Suggestion: It is forbidden because it produces sounds! (The nuts collide, or they are rolled on boards.)

Rejection: No, [they are rolled on the ground.] It is a decree lest they even out holes in the ground.

Support: Rav Yehudah forbids women to play with apples on Shabbos.

This does not produce sounds. We must say that it is forbidden lest they even out holes.

Shabbos 95a: Ameimar permitted Ributz (sprinkling in the house, to prevent dust from rising) in Mechuza.

(Ameimar): Chachamim forbade this lest one even out hollows [in an earth floor]. In this city, there are no hollows. (All the houses had stone floors.)

Rishonim

Rif (35b): (His text was unlike ours.) We answered that Rav Yehudah forbids women to play with nuts because it makes pleasant sounds. Shmuel forbids playing with apples lest they even out holes.

Rambam (Hilchos Shabbos 21:2): One who evens out holes is liable for plowing.

Magid Mishnah: In the field he is liable for plowing. In the house he is liable for building.

Rambam (ibid. 3): Women may not play with nuts on Shabbos lest they even out holes in the ground.

Rivash (394): The Rambam connotes that it is not a Pesik Reishei. If so, he should permit, for we hold like R. Shimon, who permits Ributz without concern lest one even out holes, for he does not intend! If there was no possibility of evening out holes in Ributz, why did he need to say that he does not intend? I answer that Stam, one who sweeps wants to make the floor nice, so this is considered like intent to even out holes. The other Poskim forbid sweeping because it is a Pesik Reishei.

Rosh (10:20): R. Chananel forbids producing any sound. The Gemara brought several proofs, and we do not rely on the flimsy rejections given. The Rif permits producing sound.

Poskim

Shulchan Aruch (OC 337:2): One may not sweep the house, unless the floor is paved.

Rema: Some are stringent even if the floor is paved. This is the custom. One may not deviate.

Beis Yosef (DH v'Chasav Od): Hagahos Maimoniyos bring that Sefer ha'Terumah forbids even a paved floor, for there is still concern for evening out holes between the layers, or we decree due to an unpaved floor, just like we decree [against dragging a bench] on a stone Aliyah [second story] due to a regular Aliyah (Shabbos 29b). Ameimar did not decree, because his entire city had paved floors. We do not decree about one city due to other cities. In any case, one may sweep the crumbs off a table or box. They are not special for this. There is no reason to decree about this.

Shulchan Aruch (338:5): One may not play with nuts, apples, etc. lest one even out holes.

Tur: R. Chananel forbids playing with nuts and similar things because they produce sound. The Rif forbids lest one even out holes.

Beis Yosef (DH Ein Sochakim): The Tur did not need to mention apples because all forbid lest one even out holes. R. Chananel forbids playing with nuts also due to sound.

Taz (3): No, the Tur wrote 'and similar things' to include playing with apples in a way that produces sound.

Bach (DH Ein Sochakim): According to R. Chananel, Ula forbids playing with apples [on the ground] and [throwing] nuts because they collide and make [nonmusical] sounds. Rabah forbids playing with apples lest one even out holes, and throwing nuts because they make musical sounds.

Rema: This is forbidden only on the ground. It is permitted on a table.

Question: Regarding a feeding trough, we decree to forbid sweeping a Keli lest one sweep a dirt floor (324:15)! Also 337:2 connotes like this.

Answer (Magen Avraham 7): Different decrees cannot be compared.

Rebuttal (R. Akiva Eiger): Siman 337 connotes just the contrary! There, we decree to forbid a paved floor due to an unpaved floor, for people confuse different floors, but we do not decree to forbid a table due to the ground! The Beis Yosef brings so from Sefer ha'Terumah.

Machatzis ha'Shekel: Also in Siman 337, we decree due to a decree. An unpaved floor is forbidden only lest one even out holes. The Magen Avraham says that we do not compare decrees. There, different kinds of floors can be confused. We decree in Siman 324, for whether a trough is a Kli or [on the] ground, it is called a trough, so these can be confused. People do not confuse a table with the ground.

Beis Yosef (DH Kosav Rabeinu): R. Yerucham says that Poskim who permit making non-musical sounds would permit playing on a mattress. We do not decree lest one play on the ground, for this would be Gezeirah li'Gzeirah. Presumably the Rambam agrees, for he permits sweeping a paved floor. He does not decree lest one sweep a dirt floor.

Mishnah Berurah (20): We do not decree to forbid on a table or mattress lest one play on the ground, for this is Gezeirah li'Gzeirah, but we forbid a paved floor, for this is easily confused with a dirt floor.

Rema: One should not protest against women and children. It is better that they transgress b'Shogeg than b'Mezid.

Kaf ha'Chayim (39 and 308:255): Some Poskim are very stringent about playing games even during the week for it is a waste of time. If some Gedolim did so, it was to relieve melancholy. On Shabbos we allow children to play. Any adult with Yir'as Shamayim will not, for Shabbos was given to engage in Torah. We do not know how much greater is learning on Shabbos than on a weekday!

Shulchan Aruch (308:45): One may not play on Shabbos or Yom Tov with a ball.

Source (Gra DH Asur): The Yerushalmi forbids.

Beis Yosef (DH Kosav b'Agur): The Agur forbids playing on Shabbos and Yom Tov with a ball, for it becomes dirty and it is not proper to use to cork a bottle.

Magen Avraham (72): Intent does not make a ball a Kli (Shibolei ha'Leket 121). See Sa'if 21.

Machatzis ha'Shekel There it says that intent does not help for rocks.

Eliyahu Rabah (86): Shibolei ha'Leket says that a minor's intent to play with it cannot make it a Kli. Whether or not it has Toras Kli, one may not move it, for there is no need for it, and [it is not proper] even to cover. The Magen Avraham did not understand Shibolei ha'Leket.

Eshel Avraham: If he played with it on Erev Shabbos, perhaps it was prepared. This requires investigation.

Mishnah Berurah (157): Whether it is made of wood or paper it is not a Keli just because it is proper to play with it. It is Muktzeh like a rock.

Kaf ha'Chayim (257): This opinion considers anything used only for play to be Muktzeh, e.g. dice.

Rema: Some permit this; our custom is to be lenient.

Source (Gra DH v'Yesh): This opinion explains that the Yerushalmi forbids only Hotza'ah.

Beis Yosef (ibid.): Tosfos (Beitzah 12a DH Hachi Garsinan) permits carrying a ball on Yom Tov in Reshus ha'Rabim. However, in the Yerushalmi one version says that Tur Shimon was destroyed because they played with balls.

Gilyon Maharsha: Eichah Rabah (2:4) attributes the destruction [of all habitations of Yakov, i.e. the Churban] to playing with balls on Shabbos.

Question (Shach, cited by Magen Avraham 73): Tosfos permitted only on Yom Tov!

Answer (Magen Avraham 73): Tosfos discussed Yom Tov to teach the Heter to carry in a Reshus ha'Rabim. Regarding Muktzeh, Shabbos is more lenient than Yom Tov. The Yam Shel Shlomo says that even Tosfos agrees that it should be forbidden, just the custom is to be lenient.

Eliyahu Rabah (87): The Yam Shel Shlomo says that it is improper for adults, but we allow children to play with them.

Mishnah Berurah (158): This opinion says that it is not Muktzeh because it is designated for this use constantly. All forbid playing even in a Karmelis, for the ball is prone to go four Amos away and one will retrieve it. All forbid playing on a dirt floor, lest one even out holes.