Ten people are sitting in a row, and each is thinking of a negative integer no smaller than $-15$. Each person subtracts, from his own number, the number of the person sitting to his right (the rightmost person does nothing). Because he has nothing else to do, the rightmost person observes that all the differences were positive. Let $x$ be the greatest integer owned by one of the 10 people at the beginning. What is the minimum possible value of $x$

Correct question is;

Ten people are sitting in a row, and each is thinking of a negative integer no smaller than −15. Each person subtracts, from his own number, the number of the person sitting to his right (the rightmost person does nothing). Because he has nothing else to do, the rightmost person observes that all the differences were positive. Let x be the greatest integer owned by one of the 10 people at the beginning. What is the minimum possible value of x?

Minimum possible value of x = -6

Step-by-step explanation:

Since there are 10 people and the rightmost person observes that all the differences from the subtraction or positive.

What this implies is that the person on the far left side of the row will have the largest number which from the quewis denoted as x.

Thus, we can say that the person sitting to the far right end on the row will have the smallest integer.

Since we want to minimize x, and for the fact that we are told that each is thinking of a negative integer no smaller than −15, then we will have to make the rightmost person have an integer of -15.

Since there are 9 people remaining on the row, thus, we add 9 to -15 to get the integer of the person for the leftmost person which will be the minimum he will have.

Thus;

-15 + 9 = -6