If the average of three distinct integers is 37 and the least integer is 18 .what could be the greatest integer?

Solving for the third integer:
(a + b + c) / 3 = 37 (by the definition of "average")(18 + b + c) / 3 = 37 (assuming "a" is the least integer)

18 + b + c = 111

c = 111 - 18 - b (solving for the third integer)

c = 93 - b

Now, "b" must be at least 18, in which case:

c = 93 - 18 = 75

On the other hand, the largest "b" can be is when it is equal to "c" (since I am assuming that "c" is the largest integer):

c = 93 - b

c = 93 - c

2c = 93

c = 46.5

Adjusting the numbers a bit (since we need integers), in this case we get the numbers 18, 46, 47

Thus, the greatest integer can be anything in the range from 47 to 75.