Question: A table consists of eleven columns. Reading across the first row of the table we find the
numbers 1991, 1992, 1993,..., 2000, 2001. In the other rows, each entry in the table is 13 greater
than the entry above it, and the table continues indefinitely. If a vertical column is chosen at
random, then the probability of that column containing a perfect square is:

Possible Answers:
A) 4/11
B) 5/11
C) 1
D) 9/11
E) 7/11

Thanks, Craig.

Hi Craig,

To get a feel for it, you should add two columns at the beginning:

1989, 1990, 1991, ..., 2000, 2001

and envision also filling in the rows ABOVE this one with the same rules:

0	1	2	···	11	12
13	14	15	···	24	26
· · ·	· · ·	· · ·		· · ·	· · ·
1976	1977	1978	···	1987	1988
1889	1990	1991	···	2000	2001

 

Now which of the columns contain squares, and why?

Claude