Use of the article "the": the number of the other agents or the number of other agents

I have a question regarding the use of the article "the" in the following sentence. What is correct?

"[...]. The answer of each agent depends on the number of other agents answering the same."

or

"[...]. The answer of each agent depends on the number of the other agents answering the same."

I want to refer to the number of all the other agents answering the same.

depends on the number of other agents indicates all the agents. It works like this, if I say 'the fingers on my hand' it means all the fingers my hand. Therefore, if we say 'the number of' also means 'all' - the whole number of 'other agents'.

depends on the number of the other agents rather suggests they all share a single telephone number, or similar, unless we have previously defined the group of 'other agents'. No text is an island, and 'the' links the same noun phrase for as long as wish it.