I wrote the following text:

A restaurant has a fixed number of chairs. If they set/arrange them around tables with 7 capacity (put them in groups of 7), no chair is extra. If they set them around tables with 4 capacity, 2 chair is extra. If they set them around tables with 3 capacity, 1 chair is extra. How many numbers smaller than 1000 are there for the number of chairs of the restaurant?

First, I would like to know is set...around correct and common for chairs around a table? could I use arrange?

Then I don't know the related words for groups with a certain capacity, and also the words for what remains after arranging objects in groups.

Could you rewrite the text above containing idiomatic words for such a scenario?

• set or arrange. Both OK. But "7 capacity" should be "a capacity of seven" or "tables that seat seven". Also note verb-subject number agreement. "two chairs are extra" or "there are two chairs left over".
– TimR
Commented Feb 16, 2018 at 13:39
• Nobody's said it so far, but I'd strongly advise "no chairs are left over" rather than "no chair is left over". Commented Jul 3, 2019 at 2:39

Given the nature of what I think is your goal here (i.e. writing a mathematics puzzle for students), I would punctuate and employ repetition, so your students will see the pattern explictly.

Note that I am avoiding the explicit term "divide", so as not to explicitly instruct the students to perform mathematical division, and I am avoiding the more natural "remains", because of the connotation of "remainder" with "division".

To that end I would use "arrange" and "left over". Depending on your audience it may be suitable to relax the restriction of "remains".

Consider:

A restaurant has a fixed number of chairs.

• If they arrange them in tables of seven, no chair is left over.
• If they arrange them in tables of four, two chairs are left over.
• If they arrange them in tables of three, one chair remains.

The restaurant has less than 1000 chairs.

...(question discussed below)

Your final queston, "How many numbers smaller than 1000 are there for the number of chairs in the restaurant?" is tricky (although note I have change of to in for readability).

If the answer you are looking for is the number of solutions that meet the problem statements, then it is fine, albeit tricky, and some more-literal thinkers might feel cheated by such a question – perhaps that is the intent.

If, however, you want them to list the various possible numbers of chairs, you may need to be less ambiguous. If you are happy to be specific, I'd suggest an instructional footnote:

How many chairs are in the restaurant?
(There are X possible solutions; please list them all)

(You would substitute X for the right number of solutions.)

Based on the comments I would write it as

A restaurant has a fixed number of chairs. If they are set around tables with a capacity of 7 (divide them into groups of 7), no chair is left over. If they are set around tables with a capacity of 4, there are two chairs left over. If they are set around tables with a capacity of 3, one chair is left over. How many numbers smaller than 1000 are there for the capacity of the restaurant?

• I am going to guess that express use of the term divide is intentionally avoided here, because it looks like the OP is setting a maths question, and wants the reader to realise that they have to do the mathematical division. Commented Jul 2, 2019 at 20:07