Explorations at SEARCH

WEEK 1

SET and Geometry

On Monday, our observations and organizations of a SET deck yielded many statements, including the following

Conjectures & Observations

1. There are 81 cards.

2. Each card is unique. There are no duplicates.

3. Within each color there are 9 cards of each shape.

4. Within each stripe design with the same color there are 6 ovals, 6 diamonds, and 6 wavy.

5. All cards are arranged in multiple patterns: 27 of each design, 27 ovals, 27 diamonds, 27 wavy.

By Wednesday, July 1, we had changed some terminology (to match the terminology of the SET web site) and come up with the following

Observations & Questions

Observations

1. It is easier to find SETs by colors.

2. We left 6 cards when we solved all SETs.
Questions

1. How many cards would be left if we found all the sets?

2. Is it possible that there is no card left?

3. What is the maximum number of cards left if we find all sets?
Contributed By J.C and B.E.
Observations

1. We noticed there is always a set in all 12 cards.

2. It is hard to find cards in all 4 categories.
Questions

1. Why is there always a set?

2. How many sets are in the whole deck?
Contributed By R.W. and A.N.
Observations

1. Differences are easier to find than similarities.

2. I noticed that when there are less than 12 cards in the game, the game gets harder and more frustrating.
Questions

1. What are some practiced methods to find sets?
Contributed By K.M. and N.Y.
Observations

1. One card can be a part of many sets.

Questions

1. Are you guaranteed a set with 12 cards?
Contributed By A.P. and A.E.
Observations

1. Usually, out of the 4 categories, there are 3 things that don’t match up.
Questions

1. What is the probability of everything in each category being different?
Contributed By R.A. and P.R.
Observations

1. It is easy to catch a set in consecutive numbers (1, 2, 3).
Questions

1. What are the most different cards that can be in a set?

2. How many sets are there in this deck?
Contributed By M.H. and M.M.
Observations

1. If you arrange the cards in certain ways, it is easier to find a set.
Questions

1. What is the smallest amount of cards that you can start with in order to get a set?
Contributed By E.R. and K.D.
Observations

1. It can make the game easier if you use a process of elimination to find sets.
Questions

1. What are other methods that could be used?
Contributed By A.B. and N.H-B.
Observations

1. Playing competitively makes you find sets easier.
Questions

1. Why are we left without sets?
Contributed By G.C. and K.S.