# Nikolaus Conference 2009

Start a game.

### Short explanation

You will see 15 cards, distinguished by 4 properties: background- and foreground color, a letter, and strokes around the letter. An admissible triple of cards are three cards where each of these properties is either the same for the three cards or is different for any two of the cards. You have to find out the number of admissible triples among the displayed cards. This would be too easy without two extra rules: You have only 2 minutes to find out the number, and you must get it right three times in a row (such that guessing will have little chance).

### Longer explanation

In this game you will see a number of cards. They are distinguished by four properties which are needed in the definition below:

1. There are three different background colors:

 |M| |M| |M|

2. There are three different foreground colors:

 |M| |M| |M|

3. There are three different letters:

 |N| |M| |U|

4. There are three kinds of strokes around the letters:

 /M\ |M| \M/

Definition: A set of three cards of this type is called admissible, if for each of the four mentioned properties they are either identical or pairwise different.

Examples: All triples shown above are admissible (they are pairwise different with respect to one of the properties and identical in the other three properties). In the following example we have 2 admissible triples (cards 1, 2, 4 and cards 2, 3, 5):

 /N\ |N| /M\ \N/ \U/

Start a game.

Questions and suggestions to Frank.Luebeck@Math.RWTH-Aachen.De.