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Friday Puzzler -- cards on a table

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Friday Puzzler -- cards on a table

#1

Friday Puzzler -- cards on a table

Alex Y

You are taken into a room with two tables. After you are blindfolded, I deal out cards from a standard deck (52 cards; no jokers) onto one of the tables, dealing some of the cards face up and others face down. After dealing them, I count and tell you (truthfully) that there are 52 cards on one of the tables, of which 30 are face up.

Your task is to flip and/or move enough cards so that there are the same number of face-up cards on each table.

1) How do you accomplish that?

2) What is the minimum number of cards you have to handle to accomplish that?

Re: Friday Puzzler -- cards on a table

#2

Re: Friday Puzzler -- cards on a table

John Veerkamp

Dump them all on the floor = 0 on each table,

Re: Friday Puzzler -- cards on a table

#3

A creative solution, but no

Alex Y

Bonus points for outside-the-box thinking, but no, by "move" I meant "Move between tables". I didn't specify that, so full credit on part 1. But the answer to part 2 is smaller than 52, and you will have to come up with another method to do it touching fewer than 52 cards.

Re: Friday Puzzler -- cards on a table

#4

Re: Friday Puzzler -- cards on a table

bill earl

One for each of the Goldbergs, flipping as you go.

Re: Friday Puzzler -- cards on a table

#5

Sounds like a movie allusion in there

Alex Y

that went right over my head. But it sounds like you probably have it.

Re: Friday Puzzler -- cards on a table

#6

Re: Sounds like a movie allusion in there

bill earl

Movie? Maybe "Bach to the Future" or one of the Variations.

Re: Friday Puzzler -- cards on a table

#7

Correct! 


Re: Friday Puzzler -- cards on a table

#8

Would someone please explain the answer?


Re: Friday Puzzler -- cards on a table

#9

Sure *LINK*

Alex Y

But not wanting to give away more than you wanted, I'll start with explaining Bill's answer [They are usually fun puzzles all by themselves.]

The ‎Goldberg Variations is a work by Bach, consisting of 30 variations. And 30 is the answer to part two. If that is all you were asking, read no further!

This is one that twists my mind around every time I see it. In fact, it doesn't matter how many cards or coins are on the table, or how many are face up, as long as you know the number face up. However many there are, if you move that number to the other table, flipping as you move them, you will end up with the same number heads up on each table.

An informal proof may help: Let's use our example of 30 cards face up to start. Each time you move a card, you will EITHER

A; Reduce the number of face-up cards on table 1 by 1

OR

B: Increase the number of face-up cards on table 2 by 1.

but not both.

Let's say that you happened to pick up 12 face-up cards in the process of moving. Then there would be only 18 left on table 1. However, while those twelve are now face down since you moved them to table 2, the other 18 that you moved to table two are now face up.


Goldberg Variations

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