Where the Sun stands
At noon in every year from 1930 to 2035, the Sun on this date stood between roughly five and six and a half degrees of Scorpio. The ingress falls around 23 October, so the crossing is five or six days behind by this point and the sign is not open to question in any year of the sample.
That band of a little over a degree is the whole spread rather than an average. It stays narrow because a common calendar year falls about a quarter of a day short of the orbit, pushing the Sun's arrival roughly six hours later each year, while the leap day every fourth February pulls the reckoning back by close to a full day. The two nearly cancel across the cycle.
What a face is
Each sign divides into three bands of ten degrees, sometimes called faces and sometimes decans, and the division is old enough to predate the Greek material that carries most of the surviving interpretation. A position below ten degrees falls in the first band, so this birthday sits in the opening face of Scorpio throughout the sampled century.
The Chaldean order of the planets, which runs Saturn, Jupiter, Mars, Sun, Venus, Mercury and Moon and repeats through all thirty six faces of the zodiac, assigns this one to Mars. The triplicity scheme instead splits each sign's faces among the signs of its element, and Scorpio being water gives the first band to Scorpio itself. Both routes end at the sign's own ruler here, which makes this face unusually free of the disagreement that affects most of the others.
What the tradition reads into it
Since both schemes point at Scorpio's ruler, the reading depends on which ruler you take. Traditional practice uses Mars, pairing Scorpio with Aries, and reads the band through force, incision and the direct handling of conflict. Modern practice usually uses Pluto, identified in 1930, and reads it through concealment, depth and what has to be uncovered.
All of that is what a tradition attaches to the position, not a property the position has. The checkable statement is the longitude. Everything built on top of it is interpretation, and the two interpretations here differ enough that a source naming one ruler without declaring its scheme has closed a question it should have left visible.
Where the certainty runs out
The Sun is the only body a date can place. The Moon crosses the zodiac in under a month, so on this birthday it can be in any sign depending on the year, and within a single 29 October it often moves far enough to change sign. The ascendant turns through all twelve signs in a day and shifts with the latitude of the birthplace as well as the hour.
That leaves the sun sign as the component held in common with the largest number of other people and the least able to tell one chart from another. The widget above takes your year, your hour and your birthplace, returns the exact degree instead of a band, and reports the margin from that degree to the nearest sign boundary.
The margin is the figure worth looking at even on a date like this one, where it is comfortable. It tells you whether an answer would survive a correction to the recorded birth time, and for anyone working from a certificate with an approximate hour that is the difference between a result to rely on and one to hold loosely.
Questions people ask about this
What sign is 29 October?
Scorpio, in every year checked at noon between 1930 and 2035. The Sun entered the sign around 23 October in all of them, leaving five or six days of margin.
Which decan is 29 October in?
The first decan of Scorpio, the band from zero to ten degrees. The Chaldean order gives it to Mars and the triplicity scheme assigns it to Scorpio itself.
What degree of Scorpio is this birthday?
Between about five and six and a half degrees at noon across that century. The exact figure for one birth depends on the year, the hour and the birthplace.
Why do the two decan schemes agree here?
Because the triplicity route sends the first face of a sign to that sign itself, and the Chaldean count happens to reach Mars at the same point. Most faces of the zodiac are not so tidy.
Does the face change my sun sign?
No. A face is a subdivision inside a sign, so this position is entirely Scorpio. The face adds a second layer of attribution rather than moving the reading elsewhere.
What can this date not tell me?
The Moon, the ascendant, the houses and the aspects. All of those need the hour and the place of birth, and none of them can be recovered from a calendar date on its own.