In rereading parts of Harry’s thesis, I came up with what I think is a rather interesting domain to make first experiments with the ongoing framework… I’m calling it “the Bonnie & Clyde Microdomain” for obvious reasons.

Can you spot the two outliers? What is the justification for their outlier status? Here are some problems:

==

Problem 1

1

1

1

0

1

1

1

1

1

1

1

0

==

Problem 2

222

99

132

1

128

76

4

54

68

302

298

305

==

Problem 3

9

5+5

5×2

100/10

13-3

8+4

101-99+8

18×2-26

1+2+3+4

1x2x3+4

10-6+2×2

9+7-6

==

Problem 4

6/2

10/5

20/2

18/6

99/3

17/17

0/5

3/0

4/2

28/0

1/1

9/3

==

Problem 5

1+1+1

2x2x2

7/7-6

3×2+4

2+2

4+6-1

8x8x8

9-1×7

3×4+7

(40/5)/2

3x3x4x1

1+2+3

==

Problem 6

5+1

2/20

1+5

16×3

9+4

1-0

3+1

3×16

5×8

4+9

8×5

20/2

==

Problem 7

10+3

28/2-1

3+1+9

11+1+1

13×1+0

28/2-1

6×2+1

30/3+3

3×3+3+3/3

3×3+3

2x4x2

4×3+1

==

Problem 8

9-4

16×2

7+8

5+18

8+7

4-9

2×16

18+5

23×8

1+4

8×23

4+1

==

Problem 9

5+(3x(2+1))

5+(3x(2-1))

(5+3)x(2-1)-3×3

3x(8+(2x(3-2)))

17x(9/(6-3))

4+(4x(2+2))

2x(5-(2×2))

7+(2x(2+3))

64/(2x(15+17))

2x(1/(19/19))

9×9-8×7

5x(2/(9-7))

==

Problem 10

10

3x(5×2)

20/(5+5)

30/(8+2)

7/(3+4)

20/(20/2)

9x(9+1)

9x(9+2)

9+100/10

2×60/6

8x(6+4)

20/(3+7)

==

Problem 11

1+1+1

1x1x1

2x4x2

2x7x9

9x8x5

7x7x7

9-2×3

4x2x7

8x6x2

6x6x6

2x4x8

5x2x1

==

Problem 12

1+1+1+1+1+1+1+1

4+6+3+2

1+1

2+2

6+2+5+8+3+5+2

1×1

7+7+3

10+10

35-5

7+2+1

4+4+2+4

9+8

==

Problem 13

1+2+3

1x2x3

3+2+1

(1/1)+(4/2)+(9/3)

(1)+(1+1)+(1+1+1)

(((8/2)/2)/2)+(((8-2)-2)-2)+((8/2)-(2/2))

(17/17)+(56536/28268)+((17/17)+(56536/28268))

(3/3)+(3-(3/3))+3

(2/2)+2+(2+(2/2))

(4-3)+(4-2)+(4-1)

(6/6)+(6/3)+(6/2)

(1×1)+(1×2)+(1×3)

==

Problem 14

2×100+22

9×10+9

6×10+4

15×10+1

1×1+1

12×10+8

10×17+6

3+3x3x3

42×10

31×11

29×10+8

66

==

Problem 15

222

99

131

4

128

56

0

44

48

300

298

301

==

Problem 16

452

217

111

245

362

64

329

837

757

939

637

1223

==

Problem 17

222

99

131

1

128

76

4

54

68

302

298

305

NOTE: I’ll keep updating this page with small corrections and new problems. For example, Doug got the original problem 2 right on, but most answers I received weren’t on spot. That was because the original problem would only give you a vague ‘feeling’ for the outliers–and most people would not trust that feeling and go for something completely different. Doug is a Bongard problem solver and designer, of course, so his view is very sharp about ‘vague’ feelings (if this makes sense to you). I remember a BP he designed with “kind-of-small-but-not-really-small triangles versus kind-of-large-but-not-really-large triangles”. If we’re later going to test these on people, most people won’t find the “only true” outliers and suggest something crazy. (The original problem 2 is now problem 15.)

I think this domain might help us to develop slipnets that self-adjust without having to define IS-A links, or handcoded distances between links (see, for instance, chapter 6 of Harry’s thesis).

I would love (tentative) answers (with a brief justification); and perhaps suggestions of new problem sets?

By the way, one of the problem sets is, in itself, an outlier. And another has two clear answers, even though people focus on only one. Can you spot them?