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How many strings must one tie? 
Used more than 4 strings? If one ties more than four strings to the corner, even if he adds only one more string, he transgresses the Biblical prohibition of Baal Tosif. In such a case, the fringe which contains the extra string is invalid until the extra strings are removed.
Tied two sets of Tzitzis to one corner: See Halacha 7C!
May one enter one long string and then cut it? One may form the eight strings through using a single long string. This can be accomplished through taking a single long string, folding it into four, and then entering it into the corner hole. When it is folded in half after being entered into the corner hole the string has eight sides. One then cuts the top of each string, making it into eight valid strings. If one forgot and began braiding the Tzitzis prior to cutting the top of the strings, it is invalid. This applies even if one only made one loop, and on top of it a single [set of a double] knot, and then remembered. [One must undo the Tzitzis and retie it to that hole.] If however one cut the top of the strings immediately after making the loop, prior to making even a single knot on top of the loop, the Tzitzis remains valid [and one may continue with the remainder of the braid]. Certainly if one cut the strings immediately after the first knot, prior to making any loops, the Tzitzis remains valid. Nevertheless, when using a single long string that is folded to four, it is proper to initially cut the string prior to inserting it into the hole, and thus enter four separate strings into the hole.
In the event that one used five strings to make the Tzitzis braid, how is that fringe to be validated?
It suffices to cut one string off from the Tzitzis, and it is not required to untie the entire fringe, remove the string, and then retie it from the start. Some however write that one is to undo the entire fringe, remove the extra string, and then retie it.
If one added the extra string with intent that it is for mere beauty and not for the Mitzvah, does one transgress Baal Tosif?
Some Poskim rule that in such a case one does not transgress Baal Tosif. However some rule that the Tzitzis nevertheless remains invalid, as explained next.
If a string or thread accidently became tangled within the four strings, is it valid?
Some Poskim rule one may not have any extra item mixed into the Tzitzis strings while they are tied and braided, and if the Tzitzis contains such an item it is possibly invalid. This matter however has been omitted from all other codifiers, hence implying that we do not hold like this opinion. According to all, if the string became entangled in the Tzitzis after it was already braided, it does not invalidate the Tzitzis.
What is the law if the strings of two corners became tied to each other?
The Tzitzis remains valid so long as one is able to undo the knots. One is to untangle the Tzitzis prior to the blessing, as explained in chapter 2 Halacha 6!
 Admur 11/1
 The reason: In times that Techeiles was available, the Mitzvah of Tzitzis was to take two strings which are dyed with the color called Techeiles and two non-dyed strings which are called the white strings [Chutei Lavan]. However today that we no longer have any more Techeiles, one must take four white strings, as Tzitzis are invalid if they do not contain four strings. This is learned from the verse which states “Gedilim Taaseh Lecha”, and a single Gedil [which is a braid] consist of no less than two strings which are braded over each other. Now, the verses states Gedilim in plural, hence teaching that it consists of two braids, which is a total of four strings. [Admur ibid; Taz 11/13; Menachos 39b]
 Admur 11/5; Michaber 11/12; Menachos 42a
The reason: This is learned from the verse “Pesil Techeiles”, which teaches that each of the strings must be folded like a wick. [Admur ibid] Rashi in end of Shlach explains the 8 strings correspond to the 8 days between the exodus from Egypt and the singing by the Yam Suf. The Baal Haturim explains that the 8 strings correspond to the 8 limbs of a person which can sin, which are the ears, eyes, mouth, nose, hands, legs, the Erva, and the heart. Thus, the 8 strings remind a person not to sin.
 Admur 11/1; Michaber 11/12
 Other opinions: Some rule that if one adds an extra string, the prohibition is due to Chatzitza and not due to Baal Tosif. [Raavad 1/15, brought in Tehila Ledavid 11/1]
Does one transgress Baal Tosif even if he does not wear the Tallis: lt is implied that one transgresses Baal Tosif even prior to wearing the Tallis in this form, and rather the mere tying is already a transgression. Vetzaruch Iyun!
 The reason: Since one transgressed Baal Tosif, therefore the entire set is invalid. [Admur ibid; M”B 11/60] The Gemara explains that this is because it is considered as if the braids and knots were not made at all. [Menachos 40b]
 11/23; Michaber 11/13
 M”B 11/64; See Admur 11/28
 The reason why even one loop and knot invalidates: As Biblically it suffices for one to make one loop [i.e. Chulya] and one knot, as the verse simply states “Make braids” and does not state how many loops it is to contain. Therefore, as soon as one made a single loop and knot the Tzitzis is considered to have been made with invalidation, as at the time of the braiding it did not have four whole strings, but rather one string which was folded into eight parts. Therefore, even if one now cuts the heads of the strings, it is of no benefit, being that the actual braid was already made with an invalidation, and the Torah states “Taaseh Velo Min Hasuiy”. [ibid]
 Admur ibid; M”A, Levush and Taz; See M”B 11/64
The reason: As since one did not yet make the entire Biblically valid Tzitzis with an invalidation prior to cutting the tops, therefore it is not invalidated due to Taaseh Velo Min Hasuiy. [ibid]
Other opinions: Some Poskim hold that one is to undo the Tzitzis even if a knot was not made on top of the loop, being that each part of the Tzitzis must be made in a Kosher fashion. [Olas Tamid 11/8 and 10; Tosafus Menachos 39 in name of Rashi;; See Biur Halacha 11/10 “Venitku”] Some Poskim rule one must be stringent like this opinion. Chayeh Adam 11/18; Aruch Hashulchan 11/17; Chazon Ish 2/5; 3/11; M”B ibid rules to be initially stringent like this opinion]
 The reason: This is to be done in order to ensure there is no step of the making of the Tzitzis that contains invalidation. [ibid] From here we see that even the insertion of the strings into the hole is to be done with validity. [Ketzos Hashulchan 6 footnote 40]
 P”M 11 M”Z 13; Biur Halacha 11/12 “Hosif” based on Rama 10/6; Admur 10/14; Tehila Ledavid 11/1 that so applies according to those Poskim that do not rule like the Ravaad ibid
The reason: This does not involve Taaseh Velo Min Hasuy because the Gemara ibid states that so long as one transgresses Baal Tosif it is as if he has not done anything yet, and hence when the extra string is removed it is now considered that he tied the strings there. [ibid; See Admur ibid for the same explanation regarding one who tied two pairs of fringes to a corner]
How much of the extra string must be cut? Some Poskim question whether the entire extra string must be removed or it suffices to cut the strings that extend past the braids [Gedil]. [P”M ibid; Biur Halacha ibid] Some Poskim however rule that if the string remains in the braid, it is completely invalid. [Chazon Ish 3/16] Vetzaruch Iyun if according to all it suffices to simply cut the extra string from the bottom, in its area of attachment. [See Piskeiy Teshuvos 11 footnote 184]
 Chazon Ish 3/16; Piskeiy Teshuvos 11/28 based on Michaber 10/6
 P”M in introduction to Tzitzis; Biur Halacha 11/3 “Venaasu” in name of Peri Megadim; Vetzaruch Iyun from Biur Halacha 34/2 “Bealma” in name of many Achronim who argued on the Bach regarding one who added an extra Bayis to the Shel Rosh without intent for the Mitzvah.
 Tehila Ledavid 11/1 based on Raavad 1/15
 The reason: As according to the Raavad a Chatzitza invalidates the fringe. [ibid]
 See Piskeiy Teshuvos 11/28 footnote 189-190
 Admur 23/3 “Some are accustomed upon entering into a cemetery to tie the Tzitzis of two corners to each other in order to nullify the Mitzvah of Tzitzis from them [and hence allow one to enter the cemetery with the Tzitzis revealed]. However, in truth this does not help at all, as although the Tzitzis are tied to each other, nevertheless the Mitzvah of Tzitzis is not nullified through doing so, as he intends to return and untie them.” [Admur 23/3; M”A 23/1]