11. (10 points) The teacher made 50 cards, each with numbers from 1 to 50, for the 50 students in the class. Each card has one side red and the other side blue, with the same number written on both sides. The teacher placed all 50 cards on the table with the blue side up and said to the students: "Please come to the front one by one and flip the cards according to the rule: if the number on the card is a multiple of your own number, flip it, turning blue to red and red to blue." So, after all the students have followed the teacher's instructions, how many cards will have the red side up?
【Analysis】Each card, the number written on it will be flipped as many times as it has divisors. Cards that have been flipped an odd number of times will have the red side facing up, and only perfect squares have an odd number of divisors, so this problem is essentially asking how many cards have perfect squares written on them.

【Solution】Solution: Since $1 \leqslant 1^{2}<2^{2}<3^{2}<4^{2}<5^{2}<6^{2}<7^{2}<50$. Therefore, there are a total of 7 cards with the red side facing up.

Answer: There are 7 cards with the red side facing up.