# Nikolaus Conference 2009

### 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/ |

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