Some very good answers have been posted. As for Rumba, in some cases (more common in newer Rumba music) the rhythm is naturally SQQ, while in other cases it is QQS. As for the dance figures, you were probably taught them using one of the two conventions. I was taught by instructors who followed the QQS convention. I have a syllabus I purchased used from an instructor that (the syllabus) uses the SQQ convention. The instructor marked it up so that he could teach the patterns with the QQS rhythm. It's just a matter of where you start. If you listen to the music you can hear the S and you can hear the QQ. Jump in on whichever beat coincides with how you learned the figures. Once you are dancing it doesn't matter.

As for Cha-Cha, one instructor I know is very insistent (almost pedantic) in insisting that "it's Cha-Cha, NOT Cha-Cha_Cha." She breaks down the figures using the 1-2-3-4& rhythm. That is, she matches one measure of dance steps to one measure of music. If (for example) you are dancing the basic movement, it's customary to start with a side step on the 1 beat. In her approach, that's step 1. Her step 1 is on beat 1 of the music. Next comes a rock step (2-3) followed by a chasse (or side-close; I may be using the term "chasse" incorrectly) on the 4&. That finishes the measure. The next step, a side step, starts the next measure, and it also starts the rhythm again. Simple and logical, and it fits the music. In the other (Cha-Cha-Cha) approach the first side step (1) is a "prep step." Then you dance 2-3-4&-1 (or 2, 3, cha-cha-cha). That means that the basic rhythm straddles two measures: it starts on beat 2 (the up beat) and the final step is on the first beat of the next measure. A little more complicated to analyze.

It comes down to the difference between rhythm and timing. Rhythm is the pattern of slows and quicks (or quicks and ands), while timing refers to which beat you start the rhythm with. In one case (one version of the rhythm) you start (timing) on beat 1. In the other case (the other version of the rhythm) you start (timing) on beat 2. Once again, it doesn't really matter once you are dancing. Do whatever works for you.

I'm a social dancer and have read this discussion with interest.

Most music that is suitable for dancing the cha cha either has the forth beat split into two half beats, i.e. 1-2-3-4& (traditional cha cha music) or it has both the first and third beats split, i.e. 1&2-3&4 (many popular tunes). In the first case, dancing 2-3-4&1 fits and a lead in step on 1 at the start of the dance is needed. In the second case, by ignoring the split on the first beat, we get 1-2-3&4, so no lead in step is needed. There are very few tunes that are intrinsically 1-2-3&4.

I've listened to a dozen versions of Tea for Two and most of them seem to have the second rhythm, namely 1&2-3&4. So I would dance the cha cha to those starting the chassis on beat 1 without a lead in step.

As for the rhumba, both of my teachers use the QQS rhythm on 2-3-4-1 (with the slow on starting on 4 and a hip movement on 1). But they disagree on the lead in step. One advocates a lead in step on 1, which is what I've always done, but the other teacher "allows" that for beginners but says that in the rhumba one never steps on 1 and he suggests doing a lead in step on 4, with a hip movement on 1. That to me seems to defeat the whole purpose of the lead in step, which I've always thought was to satisfy the natural desire to always start a dance on 1. If one is not supposed to step on 1 in the rhumba, then one might as well forget the lead in step all together and start on 2, ideally with a hip movement on 1, rather than starting with a lead in step on 4.

If we placed a peice of paper under each foot at the toe. How many of us could do even a simple basic and still retain the peice of paper under each foot. This is for males as well as females. Men. Perform the ladies going around part of the Rope Spin and see how good you are. Whoops one step and its lost already.