## Task B-2.5.

One hundred cards are marked with numbers from 1 to 100, with the same number printed on both sides of each card. One side of each card is red, while the other side is blue. Ana first placed all the cards on the table with the red side facing up, then she flipped all the cards with numbers divisible by 2. After that, she reviewed all the cards and flipped each card with a number divisible by 3. How many cards are now showing the red side after Ana finished flipping the cards?
## First Solution.

At the beginning, all 100 cards are set with the red side facing up. After Ana first turns the cards, 50 cards with even numbers are turned to the blue side facing up, while 50 cards with odd numbers remain with the red side facing up.

During the second turn, Ana turns over all cards with numbers divisible by 3. During this turn, Ana will turn each card with an odd number divisible by 3 so that it is set with the blue side facing up. Between 1 and 100, there are 17 odd numbers that are divisible by 3 (these are the numbers: $3, 9, 15, 21, \ldots, 93$ and 99).

At the same time, Ana will turn each card with an even number divisible by 3 so that it is set with the red side facing up again. Between 1 and 100, there are 16 even numbers that are divisible by 3 (these are the numbers: $6, 12, 18, 24, \ldots, 90$ and 96).

Finally, after the second turn, $50 - 17 + 16 = 49$ cards are set with the red side facing up.