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We will be solving interesting sets as a part of this series LRDI of the Day. I will be posting a video solution by the end of the day. You can keep a track of all the sets by clicking here: LRDI of the Day

#LRDIoftheDay #20

P. C. Sorkar, the master magician from India of international repute once placed 52 playing cards on his table. Sheldon Cooper, the first of His name, Protector of the Spot was learning to shuffle the cards to learn the magic that his friend Howard had refused to teach him and started studying the patterns if he shuffled the deck in a particular manner. Initially the topmost card was picked and put back into the deck again so as to occupy the 27th place from the bottom. After this the lower most card was drawn out and inserted back into the deck so as to occupy the 26th place from the top. This set of two operations constituted what he called a shuffling.

1. The top card will be at what position after 17th shuffling?

a. 42nd from the top

b. 10th from the bottom

c. 42nd from the bottom

d. 10th from the top

2. After how many shufflings will third card from the top come back to its original position?

a. 26

b. 29

c. 52

d. 55

3. What can we say about the positions of playing cards after first 26 shufflings?

a. The card that was initially at the top of the deck will be immediately next to the card that was initially at the bottom of the deck.

b. The top 26 cards will become the bottom 26 cards, in the same order.

c. The bottom 26 cards will become the top 26 cards, in the reverse order.

d. None of the above

The Solution

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