In a version of the game of set, cards with shapes on them are dealt out and each has four characteristics:

Type of shape (Circle, Square, or Triangle)
Color of the shape (Red, Blue, or green)
Fill type (Empty, Half filled, or Completely filled)
Number of the shape on the card (1, 2 or 3)

A "set" is defined as a three card subgroup of the cards "in play" such that for each of these four individual characteristics are either all the same, or all different. (The cards could be all different on one characteristic and be same on another.)

What is the greatest number of different cards that can be "in play" such that there is no subgroup that can be designated a "set"?

if a "set" is a group of 3 cards that either have completely matching characteristics or completely different ones for each catagory then... the only way a group of 3 cards can NOT be a "set" is if it has 2 cards that match in one characteristic but differ in that characteristic with the third. for ex.

• CRE1 CRE2 CRE3 - is a set
• CRE1 CBH1 CGF1 - is a set
• CRE1 CRE2 CRH3 - is not a set (because 2 cards are empty and the 3rd is half full)

So, if this is true, then it is possible for all 81 cards to be in play and there be no "sets", if they were all arranged properly. But for the most number of cards that can be in play and still be impossible for you to create a "set" I'm guessing 16?

• if each card had 2 characteristics there would be 9 cards total and 4 would be the max # of cards you can have where there would be no possible "sets"
• if each card had 3 characteristics, 27 cards tot. 8 max.
• 4 char. 81, 16.

 

Posted by Danny on 2004-05-12 13:39:34