Estefânia has five cards marked with the letters $A, B, C, D$ and $E$, stacked in that order from top to bottom. She shuffles the cards by taking the top two and placing them, in reversed order, at the bottom of the stack. The figure shows what happens in the first two times she shuffles the cards.

![](https://cdn.mathpix.com/cropped/2024_05_01_984603b876c0bc28095bg-03.jpg?height=189&width=717&top_left_y=1376&top_left_x=772)

If Estefânia shuffles the cards 74 times, which card will be on top of the stack?
A) $A$
B) $B$
C) $C$
D) $D$
E) $E$
Solution

## ALTERNATIVE E

The reader can verify that if Estefânia shuffles the cards 6 times, they will return to their initial position. Since $74=12 \times 6+2$, shuffling the cards 74 times has the same effect as doing it twice, which leaves the card $E$ at the top of the pile.

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