Hi, Bill,
You asked:
1) why would you suggest prepositions or conjunctions, rather than
interjections?
Because prepositions are an integrated part of speech, part of the
grammatical structure of a sentence, whereas interjections are extraneous.
2) I don't believe that, for the 4 panel cards, every "possible"
combination is included. As a matter of fact, I'm fairly certain that they
aren't. It was one of the reasons I needed to create the chart, because
there wasn't a specific "formula", as far as I could tell, for deciding
which card combinations were included. Maybe when the Looneys get back from
GenCon, if Andy sees all this, he can explain how the four panel
combinations were derived. :-)
If you lay them out in groups, you'll find that every card has four
different images, in 5 pairs, where each pair omits a different one of the 5
images of the set; and each image occurs the same number of times, but with
4 on the right and 4 on the left. So the cards do constitute a set of all
different combinations, though not in every possible different relative
position. Each individual image can be seen as occurring the same number of
times in all possible different positions on the 4 corners. Evidently an
intriguing neighboring protocol was used: where they occur on the same
card, stars and fish are always together; flames and flowers are always
together; ditto rainbow and flame. With everything in the deck being in
groups of 5 or 10 or 15, this arrangement of the 4-panel set was the most
effective way to have all different combinations on just 10 cards. Quite a
brilliant solution, wouldn't you say? If I've missed part of the formula,
I'd love for Andy to explain it.
You've probably noticed that all the 2-panel cards are a distinct pair, and
all possible pairs occur once, both in the horizontal and in the vertical
divides. In fact, such pairings always produce a triangular number, as in
standard dominoes, hence 10 cards: 1/2, 1/3, 1/4, 1/5, 2/3, 2/4, 2/5, 3/4,
3/5, 4/5.
Isn't this just the greatest fun? You can implicitly teach group theory,
systems thinking, combinatorics, and organizing by matching elements.
-- Kate
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