This question asks the minimum number of new people (denoted by *n*
in the problem) that solves the problem to generate a revised number of people
once *n* new people are added to the original 144. To complicate
matters, each new (or *n*) person carries a coin or multiple coins and
the problem requires that once the *n* new people are added, each person
in the room gets a *presumably* equal distribution of the coins so that
the final tally of people in the room each has two coins. We can construct a
spreadsheet to determine the minimum number of people (*n*) that are
introduced into the room with the coins.

However, from there, there are some qualitative, rather than quantitative,
assumptions to be made because we are not told the maximum number of coins each
*n* incremental coins could carry. For instance, we can solve the
problem by assuming *n* is 1. This means that when the new person enters
the room, he or she brings the total number of people in the room to 145 (the
original 144 plus 1). If the number of people in the room is 145 and each
person has two coins, that implies that *n—*the one additional person
who entered the room—brought 290 coins. While this is certainly possible, it
seems unlikely. Therefore, *n* is probably greater than 1 (one). We can
also discard any answer where the number of coins per *n* results in a
fraction (as illustrated when *n* equals 5 or 7), as we know that people
do not carry fractions of coins. An iterative process can be used to find the
minimum possible value of 2*n* + *k*.

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