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Set problems (Posted on 2004-05-12) Difficulty: 3 of 5
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"?

No Solution Yet Submitted by Gamer    
Rating: 4.5000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
definition of a "set"? | Comment 12 of 13 |

I'm not sure of what exactly is a "set".  I wish you would have given an example of a set.  Sorry but English was not my gooder subject. 

I would like to think that if I get any 3 cards in play with one identical characteristic, that this would make a subset.  In this case the answer is 6.

But if it is like it appears to me, that either 3 identical cards form a subset or 3 completely different cards form a subset.  This is more difficult, and worked from the opposite end to form the completely different subset.  I could play two identical cards of every type as long as I do not allow a variance for one characteristic.  So let's say no 2's or 3's are in play.  That should leave 24 cards that are not completely different, and if two of each card are in play, the answer is 48.

Of course it could be that because I have never even heard of, much less played a game of set, that I completely have no idea of what I am talking about.

Edited on August 24, 2004, 5:08 am
  Posted by Bruce Brantley on 2004-08-24 04:49:10

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