Math Is Fun Forum

easilydoctor

Member

Registered: 2007-11-18

Posts: 5

Easy Challenge Problem You Can't Solve

This is easiest problem that you probably can't solve.

"Twenty coins are placed on the top of a table in a completely dark room so that exactly 13 of them have "heads" facing upward. You cannot see the coins to determine which coins are "heads", nor can you tell "heads from "tails" by touch. You are allowed to change the "head/tail" status of as many coins as you wish by flipping them. Explain how you can separate the coins into two piles and be guaranteed that each of the piles has the same number of "heads" facing upward."

NullRoot

Member

Registered: 2007-11-19

Posts: 162

Re: Easy Challenge Problem You Can't Solve

Nice one!

If you're looking for a hint, then consider the possibilities if you removed 7 random coins or more into another pile. What are the number of heads and tails in that pile compared to the other? How would the relationship between the two change if you flipped over the coins in one pile or the other?

If you want the answer:

---

Trillian: Five to one against and falling. Four to one against and falling… Three to one, two, one. Probability factor of one to one. We have normality. I repeat, we have normality. Anything you still can’t cope with is therefore your own problem.