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I'm reading Harry Potter y la piedra filosofal, and I'm a bit confused about how this passage works gramatically:

La profesora McGonagall los observó mientras convertían un raton en
una caja de rapé. Sumaba puntos la belleza de las cajas, pero los
restaba que tuvieran bigotes.

First, is Professor McGonagall the implied subject of sumaba? If so, how does la belleza de las cajas fit in? I would have though you'd need a preposition in there, something like sumaba puntos por la belleza de las cajas.

And finally, I'm confused about how que tuvieran bigotes works; I again would have thought you'd need a preposition, e.g. something like los restaba por las (cajas) que tuvieran bigotes.

Gracias!

The sentence:

Sumaba puntos la belleza de las cajas, pero los restaba que tuvieran bigotes.

is perfect as is, and I wouldn’t go so far as to criticize the translation.

The first part of the sentence is a case of subject/predicate inversion, and is to be understood as follows:

La belleza de las cajas (subject) sumaba puntos (predicate).

This inversion is very usual in Spanish.

In the second part of the sentence, we find a nominal clause as subject, and in this case inversion is not mandatory but convenient:

Que tuvieran bigotes (subject) los restaba (predicate).

The sentence is fine as stated because reference is being made to the rules by which the students would be assessed, and by omitting “the teacher” the rules sound more impersonal and objective. This would be a literal translation:

• The beauty of the boxes added points, but the fact that they had whiskers subtracted them.

The original is in the passive form, which is in line with the idea that some impersonality was meant to be assigned to the sentence:

Points were given for how pretty the snuffbox was, but taken away if it had whiskers.

Based on the comment OP made in a different question ("I understand what the passage means, I'm just confused about how the Spanish grammar works"), I propose another way of analyzing the second sentence. To me it's clear that this is neither an impersonal sentence nor is the subject implicit.

The sentence consists of two propositions coordinated by the conjunction pero:

1. sumaba puntos la belleza de las cajas


2. los restaba que tuvieran bigotes

In (1) the subject is «la belleza de las cajas». It's after the verb instead of before, but that's not unusual in Spanish. What this proposition means is that "the beauty of the boxes added points", i.e. when there was beauty in the boxes, that beauty counted for more points. Puntos is the direct object of sumaba.

In (2) we have a plural 3rd person pronoun, los, which stands for puntos and is the direct object of the verb restaba. The subject in this proposition is the subordinate phrase «que tuvieran bigotes». That is: "that they had whiskers (or "having whiskers") subtracted them (=points)".

"Normalizing" and making everything explicit, this would be

La belleza de las cajas sumaba puntos, pero que tuvieran bigotes los restaba.

Basically, it is saying the following:

The professor awarded points to the students based on the beauty of their boxes
and took off points if the boxes had whiskers (imagine a mouse's whiskers...)

And for the following:

los restaba que tuvieran bigotes

First of all, "los" refers to the points and not the boxes, so using las is inappropriate in this case. It's already clear what he is taking the points off for (the boxes) so it is unnecessary to repeat it. No other prepositions are needed to clarify in Spanish, though from an English perspective, it is a different way of employing language.

I think, it is a rather lousy translation. I haven't read the English version but anyway, the translator could (as you well said) add one or two prepositions and make the passage a little more clear. However, as it is, i would interpret the text in these two ways:

1. 
   

   La profesora McGonagall es el sujeto implícito en la segunda oración

   
   
   

   
   

   La profesora McGonagall los observó mientras convertían un ratón en una caja de rapé. [La profesora McGonagall] Ssumaba puntos [por] la belleza de las cajas, pero los restaba que [porque las cajas] tuvieran bigotes.

   
   

   
   


2. 
   

   El sustantibo implícito de la segunda oración es abstracto

   
   
   

   
   

   La profesora McGonagall los observó mientras convertían un ratón en una caja de rapé. [Se] Ssumaba puntos [por conseguir] la belleza de las cajas, pero los [se] restaba que [porque las cajas] tuvieran bigotes.