# Inverted playing card puzzle

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?

**Just take top 15 cards from the pile and reverse them,**

now you will have two piles of 15 cards and 37 cards and both of them will have same number of inverted cards.

Inverted Playing card puzzle explanation:

Lets say there were n inverted cards initially in top 15 cards,

obviously

In remaining 37 cards number of inverted cards will be 15-n, as total 15 inverted cards.

Now on reversing the 15 cards number of inverted cards would become 15 – n and number of inverted cards will become same in the two piles.

Let’s say in top 15 cards there came 2 inverted card originally. So, after inverting this pile of 15, we’ll have 13 inverted cards in first pile and 8 in the other.

Moreover you mentioned in the 37 card pile there will be 15-n inverted cards. Which is not the case with above example.

I my opinion above answer by

In your statement,

in 15 there are 2 inverted so after invert = 13 Inverted

In the remaining bundle of 37 cards, We are left with 13 inverted cards.

So number of inverted cards in both bundle are same

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It would be 10 cards.

Remove top 10 cards from the pile and invert them.

Suppose there are n inverted cards in those 10 cards.

So the number of inverted cards in both the deck is 10-n.

Example: Let’s suppose there are n = 1 inverted card in the 10-card deck.

So, after inverting that, the number of cards inverted becomes 9. Same as the number in the 42-card deck.

### Your Answer

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