Solve the problem.
-A cell has at least 3 and at most 47 nucleii. How many cells must a scientist view under his microscope to be certain that at least two cells have the same number of nucleii?
A)45 cells
B)44 cells
C)47 cells
D)46 cells

Question

Quizplus · Accepted Answer

The pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item. In this case, there are 45 possible numbers of nucleii a cell can have (from 3 to 47, inclusive). To guarantee that at least two cells have the same number of nucleii, one must view 46 cells. This is because viewing 45 cells could, in the worst-case scenario, result in each cell having a unique number of nucleii. Viewing one more (46th) cell ensures that at least two cells will have the same number of nucleii.

Solve the Problem. -A Cell Has at Least 3 and at Most 47