(In reply to
Some statistics by Charlie)
* 28 49 97 67 84
67 28 49 84 97
67 97 28 49 84
84 97 49 28 67
97 67 28 84 49
* 47 33 87 60 34
60 33 34 87 47
47 33 34 87 60
* 56 3 88 45 57
* 17 19 61 7 100
7 17 100 61 19
* 94 89 86 95 39
* 85 39 46 83 63
39 46 83 63 85
83 85 39 46 63
* 42 14 67 1 31
42 67 1 14 31
14 67 1 31 42
42 1 31 67 14
* 59 35 68 55 29
29 68 59 55 35
35 55 29 59 68
* 22 44 37 99 34
34 22 37 99 44
* 37 98 30 27 24
27 24 30 98 37
* 67 53 94 46 59
53 46 94 59 67
* 32 18 9 82 47
32 18 9 82 47
47 9 82 18 32
* 46 35 5 97 60
* 28 47 34 85 71
47 28 71 34 85
71 28 34 85 47
85 47 34 28 71
* 89 21 12 47 13
13 12 89 47 21
* 16 50 84 69 78
* 6 24 60 99 79
79 99 60 6 24
* 18 61 66 93 51
* 53 39 49 82 91
39 82 91 49 53
* 63 97 15 90 95
* 39 98 41 69 58
41 98 39 58 69
69 98 39 41 58
* 39 50 75 68 53
50 39 53 68 75
* 1 65 89 34 46
46 89 65 34 1
* 91 53 47 19 57
* 24 52 75 6 56
56 75 52 6 24
* 45 52 26 65 34
45 26 34 52 65
* 64 84 34 26 13
26 13 84 64 34
* 81 36 58 26 40
40 81 36 26 58
58 40 26 36 81
* 89 33 23 9 31
9 23 89 31 33
* 95 4 93 20 23
4 93 20 95 23
* 62 20 63 51 25
20 63 51 62 25
* 12 69 16 17 3
3 12 16 69 17
* 18 23 49 66 74
18 74 49 66 23
* 47 33 74 100 20
74 20 47 100 33
74 20 100 33 47
* 78 19 16 63 23
16 63 78 19 23
* 84 48 11 72 83
* 36 17 70 65 90
90 17 65 70 36
* 82 23 90 84 14
82 84 14 90 23
* 9 25 23 8 60
8 9 60 23 25
* 50 30 61 2 46
* 9 54 59 92 49
* 25 100 34 46 93
34 100 93 25 46
* 45 77 13 24 81
45 81 13 77 24
81 24 13 77 45
* 9 23 5 24 40
23 9 24 5 40
* 71 60 90 80 63
63 71 80 60 90
* 74 98 27 32 60
27 98 60 74 32
* 96 95 72 34 12
96 72 95 12 34
* 51 9 29 35 92
92 9 51 35 29
35 29 92 9 51
* 86 22 8 37 77
77 8 86 37 22
77 22 8 86 37
* 97 65 48 27 24
48 97 24 27 65
97 27 24 65 48
* 73 75 17 71 15
15 71 75 73 17
* 28 49 31 89 68
68 31 28 49 89
68 89 31 28 49
89 28 31 49 68
* 66 86 34 35 87
34 66 86 87 35
* 83 85 72 51 39
85 51 39 83 72
39 51 83 72 85
72 85 83 39 51
* 65 11 24 78 7
65 7 11 78 24
* 38 4 71 49 72
* 45 41 80 78 58
78 41 45 80 58
41 45 78 58 80
* 38 9 57 44 37
* 64 61 54 70 7
* 32 68 73 84 64
* 7 67 92 97 64
* 55 76 24 62 50
* 52 37 34 30 45
34 30 37 45 52
* 84 37 10 66 79
* 45 5 80 57 51
* 85 52 87 38 16
87 52 85 16 38
85 16 87 38 52
* 12 72 13 24 9
12 72 9 13 24
* 44 37 64 85 58
64 44 37 58 85
37 85 58 44 64
* 97 98 56 45 61
45 98 56 97 61
* 63 23 86 38 55
63 55 23 38 86
63 55 23 86 38
63 86 23 38 55
38 23 86 55 63
* 1 15 82 46 79
79 1 82 46 15
* 48 8 24 3 27
27 8 3 24 48
* 38 54 83 7 70
83 70 54 38 7
* 69 25 47 78 84
84 47 78 25 69
84 69 78 25 47
25 78 69 47 84
* 90 46 26 35 77
35 90 26 77 46
* 86 18 42 32 66
86 42 32 18 66
32 66 86 18 42
66 18 42 32 86
* 1 76 52 86 93
76 52 93 86 1
* 68 96 19 28 86
68 86 19 96 28
* 97 75 7 34 24
24 75 97 7 34
75 97 7 34 24
* 4 10 76 68 91
4 91 76 68 10
* 14 92 67 79 25
67 92 14 79 25
* 63 59 7 50 79
* 59 90 82 70 58
59 58 82 70 90
* 7 12 62 54 23
12 62 7 54 23
* 74 67 99 39 2
* 82 78 54 26 28
26 54 82 78 28
* 10 67 81 6 76
6 76 81 67 10
* 96 47 80 66 19
96 80 47 66 19
* 16 81 63 51 77
* 47 37 35 34 77
35 37 77 34 47
* 76 63 41 10 37
* 21 69 41 62 95
41 21 62 95 69
95 21 69 62 41
95 41 21 69 62
* 48 76 96 13 50
* 24 18 78 92 11
11 92 78 18 24
* 44 66 52 83 90
52 44 66 83 90
83 44 90 52 66
* 64 75 91 62 85
62 85 75 64 91
* 27 14 78 6 82
78 6 14 82 27
* 13 12 35 28 6
12 6 13 28 35
* 67 94 100 69 39
* 37 66 86 97 65
* 95 73 29 9 72
95 9 73 72 29
* 48 20 18 24 78
78 24 20 18 48
18 48 78 20 24
* 93 30 22 9 49
22 9 93 49 30
93 9 22 30 49
* 49 32 2 28 59
* 87 12 2 50 92
50 87 92 2 12
* 76 87 83 53 40
83 40 76 87 53
87 83 40 53 76
40 76 83 53 87
* 83 66 23 97 34
66 97 23 83 34
* 67 82 64 25 42
82 42 67 25 64
64 42 25 67 82
67 82 25 64 42
* 38 74 88 99 53
53 88 38 74 99
74 38 99 53 88
88 74 38 99 53
99 53 38 88 74
* 96 46 76 95 82
* 76 48 16 36 98
98 16 76 48 36
36 98 76 16 48
* 65 49 9 85 5
5 65 85 49 9
* 40 21 12 60 98
40 60 12 98 21
98 12 21 60 40
98 12 40 21 60
* 6 8 41 68 81
6 41 81 68 8
* 55 13 37 41 96
96 55 41 13 37
41 13 96 37 55
* 52 60 81 77 28
81 77 60 28 52
28 60 77 52 81
52 28 81 77 60
* 7 43 8 11 46
7 43 8 46 11
* 79 58 8 42 57
* 62 18 80 70 63
* 12 22 91 80 48
48 80 91 12 22
* 82 37 90 96 25
82 96 90 25 37
* 68 47 4 95 19
68 47 4 95 19
* 71 70 74 52 65
52 70 65 71 74
* 32 84 62 47 74
47 62 74 32 84
74 47 32 84 62
74 62 32 84 47
* 11 44 37 25 27
25 11 27 37 44
* 15 88 100 42 78
* 2 78 74 7 57
2 78 57 74 7
* 3 47 68 69 13
47 68 69 3 13
* 6 50 71 87 68
87 50 68 71 6
* 36 24 26 89 87
26 87 89 24 36
* 47 50 62 60 78
60 50 62 47 78
* 29 33 45 54 50
29 45 50 33 54
* 29 20 8 33 85
8 29 85 20 33
* 62 76 68 87 65
65 76 62 68 87
* 66 26 49 94 62
94 66 26 62 49
26 62 94 49 66
* 13 87 5 80 36
36 5 87 80 13
87 80 5 13 36
* 12 73 71 100 39
* 57 45 28 32 75
32 75 45 28 57
45 57 32 28 75
57 28 32 75 45
* 25 6 62 17 54
17 6 62 54 25
* 1 76 46 21 33
21 76 46 1 33
33 1 21 76 46
76 1 46 33 21
* 6 8 93 5 98
5 6 98 93 8
* 2 34 22 49 66
22 66 49 2 34
34 22 2 66 49
34 49 2 22 66
66 2 49 34 22
* 14 91 41 17 9
91 17 14 9 41
9 41 14 91 17
* 89 25 54 17 80
54 17 89 80 25
* 100 6 9 83 78
6 83 78 100 9
* 34 65 17 99 33
17 33 65 99 34
* 8 91 87 61 70
87 91 61 70 8
* 97 24 6 92 85
92 97 85 6 24
* 19 72 67 63 3
67 63 72 3 19
* 97 91 24 50 88
* 46 100 23 88 11
46 100 88 11 23
100 88 11 23 46
* 36 45 62 94 91
62 91 36 94 45
91 94 36 45 62
* 90 16 88 69 9
69 9 88 90 16
* 31 53 64 71 30
71 31 64 30 53
31 30 53 64 71
* 30 42 36 64 66
30 66 64 36 42
30 36 64 42 66
* 40 48 32 76 94
40 32 94 76 48
* 57 13 26 88 66
66 13 57 88 26
* 35 39 96 63 29
96 39 35 29 63
29 63 96 35 39
* 72 86 10 59 94
86 72 94 59 10
* 12 81 22 100 32
22 81 100 12 32
* 34 52 72 56 68
34 56 68 52 72
* 54 76 42 62 88
54 76 62 42 88
62 42 88 54 76
* 17 7 25 48 19
25 19 7 17 48
7 48 19 17 25
* 78 9 34 72 15
9 78 72 34 15
78 9 15 72 34
* 36 63 78 43 39
43 39 36 63 78
78 36 43 39 63
* 20 38 89 42 9
38 89 9 42 20
9 38 89 20 42
* 99 46 74 29 22
74 99 22 29 46
* 62 97 73 78 55
78 55 62 73 97
* 64 60 69 49 7
* 83 73 43 36 87
73 36 83 87 43
* 13 96 81 67 55
81 96 55 67 13
* 43 42 1 27 34
* 78 95 62 96 10
95 62 96 78 10
* 65 74 25 59 34
59 65 25 74 34
* 45 99 98 62 54
54 45 99 98 62
* 16 38 96 18 59
96 16 59 18 38
96 18 16 38 59
* 36 46 60 84 28
46 28 84 36 60
60 46 36 28 84
* 87 9 38 84 88
* 19 92 95 61 12
61 12 92 95 19
* 10 78 35 51 34
35 34 78 10 51
78 51 35 10 34
* 8 64 34 2 78
2 78 64 34 8
* 48 13 86 84 90
* 45 53 25 64 58
64 25 58 53 45
25 58 53 45 64
* 44 27 30 57 82
44 27 30 82 57
57 27 82 30 44
* 36 55 44 60 8
* 39 17 91 90 95
95 90 91 17 39
* 67 7 64 35 93
* 22 71 87 38 9
71 9 38 87 22
71 22 87 9 38
* 67 45 55 17 95
The statistics for number of legitimate chosen sets that lead to the given clue set are:
0 1 2 3 4 5 total trials
111 241 93 41 13 1 500
That prize-winning 5-ways-to-get-there set was 36 15 71 93 54, where any one of the numbers could have been the one chosen by B as the clue card.
So these 500 "possible" sets of 5 can represent any of 241 + 93*2 +41*3 + 13*4 + 1*5 = 607 originally chosen sets by the audience (with B's addition). I put "possible" in quotes, as the ones with zero ways of getting there are, by the rules, impossible. The ratio 607/500 = 1.214 compares to P(100,4)/C(100,5) = 1.25. If we tried more, the ratio would likely get more closely approximated.
DECLARE SUB permute (a$)
match$ = "1234,1243,1324,1342,1423,1432,2134,2143,2314,2341,2413,2431,"
match$ = match$ + "3124,3142,3214,3241,3412,3421,4123,4132,4213,4231,4312,4321"
chc = 100
CLS
OPEN "cardtric.txt" FOR OUTPUT AS #2
FOR trial = 1 TO 500
list5$ = ""
PRINT #2, "*";
FOR i = 1 TO 5
DO
n = INT(RND(1) * chc + 1)
nn$ = CHR$(n)
IF INSTR(list5$, nn$) = 0 THEN
list5$ = list5$ + nn$: PRINT #2, n; : EXIT DO
END IF
LOOP
NEXT
PRINT #2,
'CLS
list5h$ = list5$
mct = 0
DO
FOR i = 1 TO 4
n = ASC(MID$(list5$, i, 1))
cd(i) = n
orig(i) = n
NEXT
propExtra = ASC(MID$(list5$, 5, 1))
DO
done = 1
FOR i = 1 TO 3
IF cd(i) > cd(i + 1) THEN SWAP cd(i), cd(i + 1): done = 0
NEXT
LOOP UNTIL done
seq$ = ""
FOR i = 1 TO 4
FOR j = 1 TO 4
IF orig(i) = cd(j) THEN seq$ = seq$ + LTRIM$(STR$(j))
NEXT
NEXT
Z = (INSTR(match$, seq$) + 4) / 5
cd(5) = cd(1) + chc
FOR i = 1 TO 4
IF cd(i + 1) - cd(i) > 24 THEN ak = cd(i): EXIT FOR
NEXT
newNumb = ak + Z
IF newNumb > chc THEN newNumb = newNumb - chc
IF newNumb = propExtra THEN
mct = mct + 1
FOR i = 1 TO 4
PRINT #2, " "; orig(i);
NEXT
PRINT #2, " "; newNumb
END IF
permute list5$
'LOCATE row, col
'FOR i = 1 TO 5: print#2, ASC(MID$(list5$, i, 1)); : NEXT
'row = row + 1
'IF row > 47 THEN
' col = col + 21: row = 1
'END IF
REM
LOOP UNTIL list5$ = list5h$
oct = oct + 1
ctr(mct) = ctr(mct) + 1
NEXT trial
FOR i = 0 TO 5
PRINT #2, ctr(i);
NEXT
PRINT #2, , oct
CLOSE
END
SUB permute (a$)
DEFINT A-Z
x$ = ""
FOR i = LEN(a$) TO 1 STEP -1
l$ = x$
x$ = MID$(a$, i, 1)
IF x$ < l$ THEN EXIT FOR
NEXT
IF i = 0 THEN
FOR j = 1 TO LEN(a$) 2
x$ = MID$(a$, j, 1)
MID$(a$, j, 1) = MID$(a$, LEN(a$) - j + 1, 1)
MID$(a$, LEN(a$) - j + 1, 1) = x$
NEXT
ELSE
FOR j = LEN(a$) TO i + 1 STEP -1
IF MID$(a$, j, 1) > x$ THEN EXIT FOR
NEXT
MID$(a$, i, 1) = MID$(a$, j, 1)
MID$(a$, j, 1) = x$
FOR j = 1 TO (LEN(a$) - i) 2
x$ = MID$(a$, i + j, 1)
MID$(a$, i + j, 1) = MID$(a$, LEN(a$) - j + 1, 1)
MID$(a$, LEN(a$) - j + 1, 1) = x$
NEXT
END IF
END SUB
Edited on May 14, 2007, 11:48 pm
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Posted by Charlie
on 2007-05-14 23:44:58 |
re: Some statistics -- continued
