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cotpi 45 - Coins heads up

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  • iptoc
    You are blindfolded and taken into a room with two tables. There are coins scattered on one table. You are told the number of coins which are heads up on this
    Message 1 of 2 , Apr 1, 2012
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      You are blindfolded and taken into a room with two tables. There
      are coins scattered on one table. You are told the number of
      coins which are heads up on this table. The second table is
      empty. You are allowed to move coins from one table to another
      or flip them. Before you leave the room, there must be an equal
      number of coins heads up on each table. How can you do it?

      All coins lie flat on the table, i.e. no coin stands on its edge.
      There is no way to figure the side of a coin facing up.

      --
      Originally posted at: http://cotpi.com/p/45/
      Facebook community: http://www.facebook.com/cotpi.com
    • video_ranger
      Let D = h1-h2 be the excess number of heads on table 1 relative to table 2. D is initially H (the known number of heads) and we want to bring it down to zero.
      Message 2 of 2 , Apr 5, 2012
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        Let D = h1-h2 be the excess number of heads on table 1 relative to table 2. D is initially H (the known number of heads) and we want to bring it down to zero.

        Moving any coin from table 1 to table 2 and flipping it will decrease D by exactly 1 unit regardless of whether the coin was a head or tail.

        So one solution is to move H coins to the second table and flip them.

        Another method would be to flip H of the coins then move all the remaining coins to the second table. This is equivalent to the first method - just with the additional step of reversing the tables - or flipping all the coins.

        Mark


        --- In mathforfun@yahoogroups.com, "iptoc" <iptoc@...> wrote:
        >
        > You are blindfolded and taken into a room with two tables. There
        > are coins scattered on one table. You are told the number of
        > coins which are heads up on this table. The second table is
        > empty. You are allowed to move coins from one table to another
        > or flip them. Before you leave the room, there must be an equal
        > number of coins heads up on each table. How can you do it?
        >
        > All coins lie flat on the table, i.e. no coin stands on its edge.
        > There is no way to figure the side of a coin facing up.
        >
        > --
        > Originally posted at: http://cotpi.com/p/45/
        > Facebook community: http://www.facebook.com/cotpi.com
        >
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