Appendix B: Patterns, An Induction Game

Appendix B: Patterns

An Induction Game

Method of Scoring:

Scientists:

+1 for every correct prediction
-1 for every incorrect prediction
0 for every experiment or observation

Designer :

two times the difference between the best and worst scientist
-5 for the first dropout
-10 for every additional dropout

The induction game of Patterns was devised by Sidney Sackson and popularized by Martin Gardner in his "Mathematical Games" column in Scientific American. The analogue between the use of induction in the scientific method and the game is remarkable. One player, called "the Designer" or "Nature," secretly constructs a Master Pattern—a design composed of four different symbols in a six-by-six grid.

The design can be simply or complexly ordered, but the method of scoring encourages the Designer to be clever. The other players, called "Scientists," request information about any cell ("the experiment" or "observation of nature") at any time and ask for as much information and they want.

When a scientist believes she has guessed the Master Pattern, she draws the inferred symbols in the untested cells (marked somehow in order to identify which symbols are the inductions) and now is ready to "publish." Scientists need not take turns, and they might choose not to play.

When the scientists publish, they check their theories with the Master Pattern. If a scientist drops out of the game, she has a score of zero, but dropping out could save her from a minus score. Dropping out also penalizes the Designer’s score. The overcautious scientist who prefers not to publish will often dropout. High scorers often look for symmetry, ordered arrangements, or mathematical patterns. Low scorers often use intuition, guesses, and hunches.

Designers are rewarded for constructing patterns which can be solved by only some of the scientists. In the following game, suppose a Scientist has requested the experiments shown in Grid 1. At this point many hypotheses are possible, as shown by the Hypotheses 1-3.

Grid 1: The experiments shown to the right suggest the hypotheses 1-3 shown below. (Experiments shown are B-1, C-2, C-4, E-3, E-5, E-6, F-1, and F-5)	1		O				*
	2			D
	3					D
	4			*
	5					*	O
	6					O
		A	B	C	D	E	F

Hypothesis 1	1	*	O	O	O	O	*
	2	O	*	D	D	*	O
	3	O	D	*	*	D	O
	4	O	D	*	*	D	O
	5	O	*	D	D	*	O
	6	*	O	O	O	O	*
		A	B	C	D	E	F

Hypothesis 2	1	*	O	*	*	O	*
	2	O	*	D	D	*	O
	3	*	D	*	*	D	*
	4	*	D	*	*	D	*
	5	O	*	D	D	*	O
	6	*	O	*	*	O	*
		A	B	C	D	E	F

Hypotheses 3	1	*	O	D	D	O	*
	2	O	*	D	D	*	O
	3	D	D	*	*	D	D
	4	D	D	*	*	D	D
	5	O	*	D	D	*	O
	6	*	O	D	D	O	*
		A	B	C	D	E	F

The next experiment done should be a "crucial" one-- namely, you would want to choose a cell exhibiting a different entry in each of the three hypotheses. Any of the following experiments would select the best hypothesis: A-3, A-4, C-1, C-6, D-1, D-6, F-3, and F-4.

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