Answer:
To find the least number of pens Alice must take so that she has at least 8 pens of the same color, we can consider the worst-case scenario.
The worst-case scenario would be if she keeps picking pens of different colors until she has 7 pens of each color (since she needs at least 8 pens of the same color). After that, the next pen she picks will definitely give her at least 8 pens of one color.
So, to find the least number of pens she must take, we calculate the number of pens needed to reach 7 pens of each color and then add one more pen.
She starts with 0 pens and needs to reach 7 pens of each color. So, she needs to pick \(7 \times 3 = 21\) pens (7 blue, 7 red, and 7 black).
Now, to get at least 8 pens of the same color, she needs to pick one more pen.
Therefore, the least number of pens she must take is \(21 + 1 = \boxed{22}\).
