A very special performance

This is probably the most dramatic and effective performance children can give to their parents.

We're ready for a performance !
1. Choose 2 new players and place them in front of the class.
2. Ask a third child to carefully place hats on their heads,
so that the performers do not see their own hats,
and hide the remaining hat behind the back player.
3. A fourth child could replace you and ask the questions -
To the back child, "Do you know the color of your hat ?"
the answer will be simply "Yes" or "No".
To the front child, "Do you know the color of your hat ?"
the answer will always be "Yes".
To the front child, "What is the color of your hat ?"
Still to the front child, "Do you know the color of the hat behind you ?"
the answer should be, "Only if the back child knows himself".
Still to the front child (only if the back knew), "What is the color of his hat ?"
The answer is evidently "White", but no applause.
To the back child, "Is that the correct answer",
which is evidently confirmed and then the class applauds.
4. Repeat at will with new performers.

We're ready for a performance !
1. Choose 3 players and place them in front of the class.
2. Ask a fourth child to carefully place hats on their heads,
so that the players do not see their own hats,
and hide the remaining hats behind the back player.
3. A fifth child could replace you and ask the questions -
To the back player, "Do you know the color of your hat ?"
the answer will be simply "Yes" or "No".
To the middle player, "Do you know the color of your hat ?"
the answer will be simply "Yes" or "No".
To the front player, "Do you know the color of your hat ?"
the answer will always be "Yes".
To the front child, "What is the color of your hat ?"
Still to the front child, "Do you know the color of the hats behind you ?"
the answer should be, "Only if the player knows".
Still to the front child (only if the player behind knew), "What is the color of his hat ?"
Hold the applause.
To the player behind, "Is that the correct answer",
which is evidently confirmed and the class applauds.
Repeat for the other player if required.
4. Repeat the whole performance at will with new players.

We're ready for an audience !
Even though the 4- and 5-player game is more impressive
and more difficult to decypher,
the 3-player game already makes a very good show,
especially when performed by 5- and 6-year-olds,
and will leave the parents quite amazed and perplexed.

 With 4 players Indications can now be far more condensed -     1. Show the 4 w hats and the 3 b hats to the 4 players.     2. Use the 3 bs and 1 w for all the exercises.     3. When the w is in the back,          Answers will be "YYYY", and Colors will be wbbb.     4. When the w is in a central position,          Answers will be "NYYY", and colors will be ?wbb, or          Answers will be "NNYY", and colors will be ??wb.     5. When the w is in the front,          Answers will be "NNNY", and colors will be ???w.               (? evidently represents either of the 2 colors.)Recapitulate the process -1. The first player to see only bs knows he has a w, and     his "Y" tells all those in front that they have bs.2. The front player must remember which player was the first to say "Y" and have a w,     all the others ahead having bs.The performance is evidently as it was for 3 players.
 With 5 players Another condensed set of indications -     1. Show the 5 w hats and the 4 b hats to the 5 players.     2. Use the 4 bs and 1 w for all the exercises.     3. When the w is in the back,          Answers will be "YYYYY", and Colors will be wbbbb.     4. When the w is in one of the central positions,          Answers will be "NYYYY", and colors will be ?wbbb,          Answers will be "NNYYY", and colors will be ??wbb, or          Answers will be "NNNYY", and colors will be ???wb.     5. When the w is in the front,          Answers will be "NNNNY", and colors will be ????w.The recapitulation is the same -1. The first player to see only bs knows he has a w, and     his "Y" tells all those in front that they have bs.2. The front player must remember which player was the first to say "Y" and have a w,     all the others ahead having bs.The performance is evidently as it was for 3 players.