Posted tagged ‘Microdomains’

The Bonnie & Clyde Microdomain

April 6, 2008

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?

Advertisements