Challenge of Inverted Playing Cards

One fine day, Mr. Puzzle and Mr. Fry were playing cards, but suddenly power went off and they were getting bored. So Mr. Puzzle randomly inverted position of 15 cards out of 52 cards(and shuffled it) and asked Mr. Fry to divide the card in two pile with equal number of inverted cards (number of cards in each pile need not be equal).

It was very dark in the room and Mr. Fry could not see the cards, after thinking a bit Mr. Fry divided the cards in two piles and quite surprisingly on counting number of inverted cards in both the piles were equal.

What do you think Mr. Fry must have done?


This is what he must have done! 

  

Equating Counts of Inverted Cards in Piles

What was the challenge?

Mr.Fry must have taken top 15 cards & inverted positions of all. So he divides deck into 2 piles - one with 15 cards & other 37 cards.

Now suppose if there are 7 cards that were inverted in top 15 & 8 were inverted in remaining 37. When he flips top 15, 7 remains in normal position & 8 remains in inverted position. That is equal to 8 cards in inverted position from pile of 37 cards.

In short, if there are N cards inverted in top 15 then there are  15 - N cards inverted in remaining 37 cards. So on flipping position of top 15, there will be 15 - N cards in inverted position in top 15. That's how both piles would have equal number of inverted cards i.e. 15-N.  

 

Had Mr.Puzzle inverted positions of 20 cards randomly then Mr. Fry would have flipped top 20 cards. He would have made 2 piles with one with 20 cards & other 32 cards to equate the count of inverted cards in piles.