Random picking of hands from a database

[Troll_Inc]

I would like to choose random hands from a list of net poker hand results (see below).

1. Anyone know how to do this in Excel? There is the "Random Number Generator" in Excel, but I can't figure out how to use it for this purpose.

2. If not Excel, what is the easiest way to do this? Someone know of a website for this?


bb_won
0
-0.5
0
-0.5
0
-29.1
1
0.7
-0.5
0
-12
0
6.1
0
-0.5
20.2
-1.5
0
-1.5
0
0
2.2
-0.5
-0.2
1.9
3.2
2.5
1
-0.2
0
-0.5
0
0
0
0
0
16.7
-8.7
-0.5
-0.2
-0.2
-6
-0.5
0
-0.2
2
3.9
-0.5
0
0
0
0
0
0
-4.2
0
-0.5
-1.5
0
-0.2
2.2
-0.5
0
-0.2
-0.2
0
-0.5
-5.5
-0.5
2.2
4.7
0
0
0
0
0
-11
0
0
0
-0.2
-0.5
-0.2
9.5
-0.5
-0.5
-0.5
-0.2
0
1
0
2.9
-1
-7.5
78.8
5.3
-0.2
-0.2
-1
0
0
-0.5
-4.2
0
-4.2
0
1.5
0
0
-0.2
-25
0
3.2
0
-2.5
-7.5
-0.5
0
0
-0.5
0.7
0
-0.5
-1.5
0
-1.5
-1.7
11
0
0
0
54.7
0
-2
2.2
0.5
0
1.5
2.4
-0.2
-0.2
-1.5
-0.5
0
-0.5
0
0
0
-1.7
-10.5
21.2
-0.2
0
-0.5
1.5
0
0
0
-1.7
3.4
0
0
1.5
-7.2
0
-26
0
-0.5
0
0
0
-0.2
0
0
0
1
-0.5
1.5
0
0
-0.5
-0.5
-0.2
0
0
0
-2.5
0
4.9
0
0
0
4.7
7.4
0
0
-1
0
-0.2
0
1.5
-0.5
-0.5
-0.5
6.2
0
7.4
0
0
0
0
0
0
0
3.5
0
-7
-0.5
-0.2
-0.2
-0.5
-1.5
1.25
4
-63.2
0
-4
0
0
0
-0.2
-0.2
0
0
7.5
2
-4.5
-2.2
3.4
0
0
-5.7
-13.2
-0.2
0
0
7.2
-0.5
-2
0
0
-0.5
0
2.9
-0.5
0
0
0
3.4
-0.2
0
38.9
0
-0.5
-4.5
0
-9.2
2.5
-0.2
-0.5
-1.5
-1
-0.5
-1.5
0
4.5
0
-0.2
0
0
-0.2
0
-6.2
-2.2
0.8
-0.2
6
-0.5
-0.5
0
0
0
-0.5
-1.5
-13.4
-1
0
0
-1.5
0
3.5
-0.5
0
-13.7
0
14.7
0
0
0
-2.5
0
0
-0.2
-0.5
0
-0.2
-0.2
0
-0.5
32.2
-0.5
0
-1.7
0
-1.5
-8.5
0
-0.5
0
-1.5
0
44.6
1.5
-2
0
0
-0.5
0
2.9
-0.2
4
0
-0.5
-0.5
-1.5
-0.5
0
0
-0.5
0
-1.7
0
-0.5
0
-7.7
0
0
6
-0.5
-0.2
0
0
-1.5
-0.5
0
-0.2
-0.5
3.9
5
0
0
19.6
-0.5
0
-0.5
-0.5
0
0
-0.5
0
-0.2
-1.7
-0.5
0
-0.5
0
-2.2
4.9
-8.5
0
-0.5
-0.5
0
0
-0.5
-0.5
0
0.5
0
0
0
38.7
-3
-1
0
0
0
-0.2
0
0
-1.7
-0.5
0
-0.2
0
-10
-0.2
35.6
-0.5
0
-9.2
0
0
0
-2
0
0
-0.2
-0.5
0
0
0
0.7
-0.5
-15
-0.5
0
0
-0.5
0
-4.5
-0.2
-3
-2.7
0
-0.5
-0.2
0
-1
-1.7
8.5
0
0
0
0
0
0
0
-0.2
0
-1.7
-2.5
0
-0.5
-0.2
17
0.5
0
-2.5
-0.5
-5.8
0
0
-0.5
0
-1.5
0
0
0
0
-4.5
0
-0.2
-5.2
-4.2
-0.2
-0.2
0
0
7.5
-1.5
0
1.9
0
-3
-7
0
0
-0.2
1.5
-0.7
-0.5
-0.2
9.2
-2.5
-0.5
-1.5
-0.2
0
0
-0.5
-0.2
3.5
-0.5
0
0
0
0
0
0
0
-2.2
-1.7
-9.2
30
-0.2
0
-2.5
-0.2
-0.5
-0.5
-0.5
0
0
0
10.1
-24
0
0
10
0
5.2
-9.5
-0.2
-9
-0.2
-0.5
0
5.7
18.8
0
-0.2
5
-1.5
-1.5
0
3
0
0
0
0
-0.2
-3.2
-1.5
0
0
-0.2
-0.5
0
-0.5
-0.5
0
-0.2
1.9
0
35.6
-6
0
-2
15.6
-0.2
0
0
-0.5
0
1
-0.2
-0.5
0
0
-0.5
1.9
0
-1.5
-0.2
0
1.5
-0.2
0
0
-0.2
-0.5
0
-0.5
64.1
0
-0.2
-14.2
-0.2
-0.5
2.2
0
-0.5
-0.5
-0.5
3.7
2.2
-1
-3
0
-0.5
1
0
-2.7
0
-0.5
-0.2
0
-0.5
0
0
0
0.3
0
-0.2
-0.5
-17.3
-2
-0.5
55.1
5.7
0
-7.4
0
0
7.2
2.7
3.9
2.5
-0.2
-0.2
-1.5
-1
-0.5
-0.5
0
0
2.7
0
0
0
-0.2
12.4
-0.2
0
0
-0.5
-0.5
1.2
-0.2
0
26.6
0
0
5.2
-0.5
-3.5
-7
0
0
-0.2
1
0.7
0
0
-0.2
0.5
-0.5
6.9
0
0
-0.5
-8.5
0
2.4
-0.2
0.2
-0.5
0
0
0
-2.7
10
4.5
0
-2
0
0.7
-1.5
0
-16
0
0
0
-0.5
0
0
0
0
0
4
-4
7
0
-8
-0.5
-0.5
0
0
0
33.3
0
0
0
0
-0.5
0
-0.5
0
0
-0.5
-0.2
-0.2
-0.5
-0.5
0
3.5
-0.5
0.7
0
0
0
0
-16.2
-0.2
-16
-1.7
0
-0.5
-0.2
0
10.5
0
0
0
0
0
-0.5
0.2
-0.2
-0.2
-0.5
96.4
-1.5
-16.2
-1.7
0
0
-0.2
0.7
37
-0.5
-10.8
0
5.5
-3.2
0
0
-0.2
0
-5
-0.5
-0.2
-0.5
0
0
6.5
0
-0.2
0.7
1.2
0
0
-1
-0.2
0
3.9
-0.5
0
33.4
0
0
0
-0.2
-34.2
-1.5
-15
0
-0.5
-0.2
3.5
-30.5
4.9
0
-3.7
0
18
-9.7
-3.5
-4.7
0
7.2
1.5
-6.2
0
0
-16.5
-2.5
56.4
-6.2
-0.5
0
2.9
2
-1.7
-22
0
-2.5
0
0
4.9
-1
8
0
-7.7
0
0
14.2
0.1
0
0
-26.3
-4.5
0
2
-0.2
-0.2
-0.5
6
-0.5
-2
0
0
-0.2
0
0
0.7
-0.5
6.4
-10.7
0
-0.5
-0.5
-3.5
1.5
-1
3.4
0
0
-7.8
0
5.6
0
-0.5
0
-1.5
-0.5
-0.5
-2
-10.2
1
0
0
3.2
14.9
9
0
-13.5
0
-0.5
2.9
55.5
-3.7
0.5
-0.5
-0.5
0
-3
-64
-124
5.5
0
-0.25
-70.25
-7
-0.5
-0.25
-0.75
0
-6.75
0
3.75
0
-1.75
15.5
-1.75
0
0
-0.25
0.25
-0.25
0.5
0
0.25
-0.5
0
-7.25
0
-0.25
0
0
0
-109.25
0
3.5
0
3
-0.25
0
0
0
-12
4.75
6
0
0
-7.5
0
0
0
0
0
-17.75
-0.5
-0.25
0
0
44.5
1.5
-3.75
-2.5
0
-0.5
66.5
-0.5
0
0
-12
5
-3
0
17.25
-0.5
-1.75
-21.25
2.5
-0.25
0
-0.5
0
0
11
0
0
0
-0.5
-6.75
0
0
0
0
6.5
-0.25
0
2.5
-2.25
-0.25
-5.5
0
-0.5
0
-0.5
-2
0
0
0
-0.25
0
0
3.5
0
-0.25
-0.25
-0.5
0
52.75
-15.75
0
-1.75
0
1
-0.5
0
0
-0.25
0
0.75
2.25
-0.5
0
-0.25
-0.5
9.25
-0.5
0
0
0
0
0
0
-3.25
-7
0
0
4
-0.25
10.75
0
-0.5
20.25
-0.5
12.25
-5
30.25
0
-2.25
-0.5
0
-1.5
0
-0.25
-0.25
-5.25
26.25
-2
-0.5
-1.75
0
-2
0
-0.25
-0.5
-2
-0.5
0
-4.25
0
0
-0.5
0
-15
0
0
0
0
0
-0.25
9
0
0
0
-4.25
-0.25
-0.5
-1.5
0
-0.25
-0.5
-0.5
0
2.5
0
-2.75
0
0
0
0
2.5
-0.25
0
-33.75
0
-1.75
-0.5
44.5
-0.25
-0.5
0
0
-0.5
0
-0.5
-9
0
0
0
-0.25
0
1.75
-2.5
0
-0.5
0
16
-0.5
-1.75
-0.5
31.5
-1.5
-20.75
-0.25
0
0
-0.25
-0.5
0
-0.5
0
9.75
0
-0.5
13.5
5.25
0
-6.5
0
-14
-5.5
0
0
-2
0
0
-1.5
3.5
0
-0.25
1
-1.75
0
-1.5
-0.5
-0.5
0
0
-0.5
0
0
-0.5
0
0
32.75
0
-0.25
9.5
0
-2
-0.5
-0.5
-0.5
0
-0.5
0
0
0
0
0
-35
0
0
0
-42
-0.25
-5.75
3
0
-0.5
0
-4.5
10
-2
-6
-0.5
0
0
0
-0.25
-5.5
-12.5
0
-4
0
0
-0.25
0
-0.5
0
-0.25
0
-3
-20.5
-0.25
-0.5
16.75
-0.5
0
0
0
0
0
0
-0.5
-0.5
0
-2
0
0
-0.25
0
0
3.5
-43.5
-5
-1.75
1.5
0
0
-0.5
-2.25
0
0
-2
-15.75
0
2
-0.25
0
-0.25
0
-0.5
4.5
0
0
0
0
0
0
8.5
-0.5
-17.75
-0.5
0
0
-1
0
-0.25
-2
-0.25
4
0
4
0
-2.25
-0.25
2
4.5
-9
-0.25
0.25
-3.5
-3
0
0
0
0
0
-0.25
12
-2.5
-0.5
0
0
-0.5
5.25
-6
0
-3.5
-2.5
-1.75
35
-0.25
0
0
-2.5
0
0
0
-0.25
-0.25
-0.5
11.5
-18
0
0
0
0
-1
-0.5
-0.5
6
-0.5
-0.25
-0.5
0
6.5
-0.5
-2
0
0
-0.5
-2
-0.5
0
0
0
6.5
-0.25
0
-3.5
-2.5
-0.5
0
-0.5
1.5
0
0
0
0
0
-0.25
0
-0.5
-0.5
0
0
0
0
0
0
-0.25
-0.25
-0.5
-0.5
-0.5
-5
0
0
0
0
0
-5.25
9.75
-1.75
0
-0.25
-0.25
0
-0.5
-0.25
0
13
2
0
0
-2.75
0
55.75
-0.5
0
-0.5
-1.5
0
-0.25
0
-0.25
-0.5
0
0
-0.5
0
-0.25
0
7.75
0
-0.25
0
-0.5
0
-0.5
6.75
0
-0.25
0
-0.5
0
0
27.5
0.5
0
0.25
0
-0.25
-0.25
-1.75
-0.5
-0.5
-0.5
0
-0.25
-0.25
-0.5
-0.5
-6.75
0
-5.5
0
-2.75
30.75
-3.25
-14.25
-0.25
-0.5
0
0
0
0
-0.25
-1.75
-15
0
0
-0.5
-0.5
-0.25
0
-0.5
0
0
0
-0.25
0
-16.25
0
0
-0.5
0
-0.5
0
52.25
-0.5
0
0
-0.25
-0.25
0
-0.25
1
0
57.25
0
-6
-28.75
0
-0.25
0
3.5
0
-0.5
2.5
0
0
0
-0.5
0
2.5
0
-2.25
-3.75
-2.75
-3
-0.25
0
-0.25
-0.5
0
-2
11
-0.25
-0.5
-0.5
0
13.75
-0.5
-0.25
0
7
0
-0.5
0
7
-17.75
2.5
21.25
1.5
-0.5
0
15.75
0
-0.25
0
-0.5
-0.5
-0.5
-0.25
-0.5
0
0
-0.25
-0.5
7.5
-0.5
0
-0.25
100
0
-1.5
0.75
0
-0.25
17.25
0
17.25
-0.5
0.5
0
12.5
0
0
-0.25
-0.25
-0.25
0
1.5
0
3.5
-7.75
-5.75
-0.25
-1.75
-5.75
0
-0.5
0
0
7.25
0
-0.25
0
-0.5
0
47
-0.5
5
-0.25
-5
0
0
-1
-0.5
0
0
1.25
-12.75
0
-2.25
16.25
0
-0.25
-0.25
-0.25
0
-2
-0.5
-0.5
0
0
-0.25
-6.25
0
0
0
118.25
-2.5
-6.25
-5.25
0
-6
-0.25
0
72.5
23.25
4
0
-3.75
-2.5
-3
0
0
-0.5
0
-5
0
0
13.75
-3
-0.25
-0.25
0
0
-5.5
-2
0
0
-3
0
0
-0.5
-4.75
9
-0.5
0
0
3.5
0
0
-0.5
-0.25
-25.5
-0.5
0
7
-2
0
15.75
0
0
0
-2
0
0
0
-0.5
0
0
0
0
-0.5
0
0
-0.25
-0.5
0
-42.5
5.75
-0.25
-0.5
0
-0.25
51.25
-8.75
31.5
0
0
-0.5
-0.25
0
0
-0.25
-0.5
-1.75
0
-0.5
-3.75
0
0
0
0
12.75
0
0
-0.25
-2.25
-0.25
0
-0.5
1
-0.25
0
-0.5
0
2.5
-0.25
0
0
8.5
-1
0
0
-0.25
-0.25
0
0
-0.5
-0.25
-2.75
0
0
-0.5
0
0
0
0
0
-0.25
0
0
4.5
41.75
-1.75
-0.25
-0.5
-0.5
0
-1.5
-14
6.75
44.25
-0.25
0
-0.5
0
0
-2.75
0
0
0
0
0
-0.5
50.5
-0.25
-0.5
-0.5
20.75
-15
-100.5
-29
-11
-0.25
-3.25
2.5
0
11.5
3
-32.5
-1.75
-4.75
0
0
0
-25
5.5
-0.25
-6.75
-6
-0.5
-15
-0.5
-0.25
-0.5
-2.25
0
10.5
-0.25
-36.5
-36.25
0
-4.5
-0.25
0
-1.5
0
-0.25
-1.5
0
4
-0.25
-0.5
78
0
7
2.5
5.5
-15.75
5
0
0
2
18.25
0
-4.25
0
4.75
-0.5
-3
-0.25
-6.75
0
-0.25
25.25
16.75
4
-5
-0.5
-55.25
0
-2.25
0
21.25
0
0
9
0
9.5
-14.5
0
-41.75
0
-24.5
0
0
0
0
4
-1.75
-0.25
-0.5
-3.75
-0.25
0
-11
15.5
4.5
2.5
0
0
-5.75
0
0
0
0
-7.5
-6
0
0
-0.5
-0.25
-55.25
-0.5
-0.5
9
-3.25
-1.75
0
-4
0
3.25
0
0
-0.25
0
6
0
-0.5
-0.25
0
-0.5
-10.5
0
2
0
0
-0.25
-0.5
-0.5
-0.5
2.25
-2.25
3.75
-0.25
-0.5
0
-0.25
0
0
0
-8
-8.5
0
0.5
-0.25
0
-2.25
-0.5
0
0
-19.5
0
69
0
0
-0.25
-0.25
23.75
0
-0.25
1
-0.5
-0.5
-0.5
8
0
0
0
0
0
0
17.25
8.75
0
-0.25
21.75
-4.25
0
4.75
-3.5
-0.25
0
0
-0.5
-0.25
15.75
0
-2.25
0
-0.5
0
0
-1.75
0
3.5
0
-0.25
4
-0.25
-0.5
0
0
0
-14.25
-0.5
13
0
0
0
9
24.5
0
-0.25
0
-0.25
33.5
-3
1.25
0
-22.5
-0.5
0
0
0
0
0
4.5
-0.25
0
-0.5
0
0
-0.5
0
0
-5
0
0
-0.5
-0.25
0
0
-1.75
-9.5
-0.25
0
-2.25
-5.25
0
23.25
-37
12.5
0
0
0
35.25
0
0
0
0
-0.25
0
0
-0.5
0
-0.25
0
12.75
-88.75
0
-0.5
0
-0.5
0
5.5
-0.25
0
-0.25
13.75
-3.25
-0.5
0
0
4
0
-2.25
0
-7.25
0
6.75
0
-0.25
-0.25
-28.5
0
0
-0.5
-0.5
-0.5
-1.75
0
0
8.5
0
-3
0
-1.75
0
-0.25
-0.25
-2.25
0
3.5
0
-0.5
-2
-1.75
0
5
0
-0.5
-2.75
0
0
0
0
3.5
0
-0.25
0
-0.5
-5.25
0
0
1.5
0
0
-1
-0.5
-0.25
1
-1.5
-9.25
-2.25
-58.25
0
0
-31.75
-2.75
-5.5
-0.25
-12
-0.25
0
15.75
-0.5
-1.75
0
0
0
-12.75
0
-0.25
-0.25
-0.25
-0.5
-0.5
-2
6.75
-11.75
0
-0.25
0
0
-4
-0.25
0
31.5
-0.25
0
-1.75
-0.5
0
-18
0
-18.75
-0.25
0
9.5
5.25
34.5
8
13.25
-20.5
0
4.75
5.5
-1.5
0
-0.5
44.25
0
-0.5
0
-0.25
0
0
8.5
-0.5
0
0
0
-0.25
0
0
0
0
-6.5
-0.5
-0.5
-2
-5.25
-0.5
-2.25
0
0
0
-17
0
0
-0.5
0
4.75
-0.25
-0.5
0
15.75
34
0
-0.25
0
-0.5
0
51.75
-25
0
0
-0.25
-42.5
0
-0.5
-0.5
5.5
-3
-99.25
-3.5
0
2.25
-0.25
-0.5
-0.5
0
-10.5
-2.75
-0.25
0
-11.25
8
0
0
0
-0.5
4
-0.25
-0.5
-15.75
-10.5
0
-0.5
-3.75
-3
0
0
11.5
-0.25
0
-12
-0.5
-0.5
-24.8
-0.2
-9.5
0
-15.6
-0.5
0.7
1
3.4
-3.5
-0.2
-33.5
-3.5
9.7
0.7
0
4.6
0
0
-8
-0.5
-4.5
-0.5
0
0
0
-3
0
0
-1
-0.5
-14
0
-0.5
-0.5
0
0
0
27
8.9
-7.7
0
12.9
0
0
-0.2
8
-0.2
-2.5
-0.5
1
0
24.5
0
0
0
0
8
-24.75
-0.25
-0.25
-0.25
-0.5
-6
0
13
-2.25
0
0
0
-0.25
12.25
-0.5
0.75
-3.5
-14.75
-9.75
0
15.75
-0.25
0
-0.5
-0.25
0
0
-0.5
-3.75
-0.5
-14
0
0
10.5
-31
-1
-0.25
-0.5
1.5
-4.7
-0.2
-12
-16.7
-0.5
-12.2
0
0
-2.2
60
-27.2
-0.2
-6
-6
-0.2
8.9
6.5
-11.7
0
-0.5
-2.2
0
1.9
-2.7
0
-0.2
-19.4
-9
0
-1.5
-21.6
3.4
0.2
-1.7
0
-0.2
-0.5
-8.2
-0.2
5.8
0
-0.5
-0.5
-0.2
0
1
-0.2
5.8
0
0
-0.2
-2.1
0
0
0
-0.5
0
0
32.2
-0.5
0
-0.2
-0.2
0
0
2
0
-0.2
4
0
5.9
-1
-1.5
0.7
0
0
0
2.4
0
0
-0.2
6
-0.5
0
-0.2
0.5
0
-0.5
5
0
-0.2
3.9
0.2
0
-0.2
-5.2
-0.5
-8
5.5
0
0
-0.2
-2.2
-3.2
-0.5
-0.5
0
0
-1.7
0
0
53.2
0
-8.7
0
0
6.1
-1.7
-0.2
-6.2
-4.5
0
-0.5
-6
-0.5
0
-5.5
0
-4.2
-0.5
-2
0
0
0
6
0
-0.5
-6.5
0
0
-0.5
-0.5
1.9
-1.7
-3.5
0
-5.7
0
1.2
-4.5
0
-0.2
0
6
-0.5
-1.7
-0.5
2.5
-50
0
-10.5
-1
0
0
0
0
-0.2
-0.5
0
-1.7
10.4
0.7
0
0
0
0
0
-37.6
0
8.1
0
0
0
0
-2.2
-0.2
-0.5
-15.1
0
0
-0.2
8
-4.2
-5
1
10.1
-1
0
0
0
-0.5
-5.2
0
-0.5
-0.2
0
-0.5
-2
0
-0.5
0
-0.2
0
0
-0.5
0
0
-0.2
0
7.4
8
0
-0.2
-8
2.5
0
-31.7
0
-3
-7.2
0.7
0
-0.5
0
0
0
0
0
1.5
7.7
-0.2
0
-0.2
-0.5
-0.5
0
0
3.9
-0.2
0
0
-0.5
-0.2
0
-1.7
0
5.3
-1
-2.7
-3.7
-4.5
0
-0.5
-0.2
0
0
0
0
-9.2
65.1
0
0
-0.2
6.5
0
-2.7
14.5
-0.2
0
0
-0.5
0
-0.2
0
0
0
0
66
3.4
0
0
0
0
3.5
0
0
-1
-1
19
0
-0.5
-0.5
-0.5
-0.5
0
0
0
0
14.2
1
0
-0.2
0
0
0
-6.8
-0.5
0
-1.7
-0.2
0
7.4
-0.5
8
0
0
0
25.8
-0.5
-0.2
0
8
-2
0
0
-0.5
0
0
0
-0.2
-3.7
-2.7
0
-0.2
0
0
-0.5
-0.5
-0.5
-10.7
0
-0.5
0
0
-9
0
5.1
0
-0.2
0
3
16.5
0
0
0
-2
-1.5
3.5
-0.2
0
-0.5
-0.5
0
0
0
-9
5.9
3.7
0.7
-5.2
-0.2
15.3
-0.2
0
0
4
0
0
-19
-6.2
-0.5
0
0
-0.5
-0.2
-0.5
1
0
-0.5
0
0
0
0
0
-3
6.5
0
-4.2
-1.5
-0.5
59.5
-1.7
3.4
-3
0
0
-0.5
5.1
4.4
0
0
1.2
11.5
-0.2
-5.5
1.5
0
18
-2.2
-35
0
-0.5
-0.2
-1.5
-0.5
4
-0.25
0
-0.25
-0.25
-1.5
-230.75
-0.5
-0.5
-0.5
-4.75
0
0
0
0
0
5.5
0
-10.75
23.75
-0.25
20.25
0
8.25
0
-2.75
-1.75
-0.25
0
0
0
69.25
0
-2.25
-25
-0.25
38.75
0
-0.5
-2.5
0
0
0
0
0
11.5
-0.25
2.75
0
-6.25
0
14
-0.5
-2.75
0
-2.75
0
0
-0.25
0
0
0
-5.25
-0.25
0
0
-1.75
0
-0.25
-2
-1.75
0
-0.5
-0.25
0
10.5
-0.5
0
-7.25
0
0
-0.5
-6.25
0
0
5.25
-1.75
-2.25
-0.5
-6.25
32.75
0
-0.25
-0.5
71
0
-0.25
-0.5
-6.25
-0.5
28.5
0
0
0
0
0
-5.5
-4.75
0
-0.5
0
0
0
-6.75
0
4
13.25
0
-0.5
2.5
-0.5
-0.5
-0.5
0
-0.5
-17.25
0
20.75
0
0
1.75
-5.25
-0.25
-3.25
0
0
4.25
0
-0.5
0
0
-0.5
-0.25
-4.5
0
-2.25
-0.5
3.5
8
-0.25
0
-0.5
0
0
6.75
17
8.5
0
0
0
27
0
0
-0.5
0
0
5.5
0
0
-2.5
5
0
2.25
0
-10.75
5.25
-0.5
0
-0.25
1.5
0
-0.25
-1.5
-0.5
0
0
0
0
0
0
48.75
7.5
-0.25
0
-0.5
-1.75
101.5
-8.5
0
0.5
-0.25
0
0
-12.75
9.5
7
0
0
0
-0.25
-1.5
0
0
-1.75
14.25
-0.25
56
-0.5
14
-0.25
-0.25
0
-11
-0.5
-2
0
0
-5.75
0
-1.5
0
-0.25
-2.75
-0.5
15.25
-6
0
4.5
0
0
0
-0.5
-16
79.5
24.25
-0.5
3.5
0
-2.5
-3.75
-0.25
1
0
0
3.5
-2.75
0
-1
0
13.5
-0.5
0
-16.75
-0.5
17
-1.75
0
-2.25
5
-1.75
-0.5
129.75
-0.25
3.5
-0.5
-4.5
3.75
-34.5
0
2
0
25
-27
0
-1.5
-0.25
0
-0.25
-5.5
2
-0.5
-0.5
2.25
3
-40.5
0
-3
-0.5
0
7.75
-0.25
-2.5
5
-2.5
15.5
0.75
-14
-5.75
0
0
0
12.75
0
0
0
0
-22.75
-17
0
0
0
26.75
-10.5
0
0
-22
-1.5
0
0
-0.25
0
-2.25
0
-0.25
-2.25
1.5
2
0
23.25
17
-31.75
0
0
0
-2.25
0
0
0
0
0
-63.75
-0.25
0
0.5
12
-1
-0.25
0
-1.75
7.5
-0.5
9.25
0
0
0
0
0
2.5
-0.25
-0.25
12.25
0
0
-12.25
0
-26
0
-0.5
-1.5
-8
6
-0.25
0
-4
-6.25
1.25
0
0
0
0
0
0
18.75
14.5
-0.25
-10.75
0
-0.25
-0.25
-0.5
0
-0.25
-1.5
0
0
-6.5
0
0
0
0
0
1.5
-4.75
-0.5
0
-2.25
-29.25
0
0
-0.25
0
0
0
-1.5
0
-0.25
-0.25
81.75
-3.75
5.5
-0.5
0
-0.5
0.75
0
0
0
39.5
0
0
3.5
13.5
-2.25
-2
1.25
7
-4.75
0
0
5.25
0
0
0
0
-7.5
-0.5
-1.5
0
-0.25
-0.5
-11.5
-0.5
-4.25
-0.5
-1
0
0
0
-0.5
23.25
0
-6.25
0
3
0
0
9.25
0
1.5
13.25
-0.5
-0.25
-2
-0.5
-6
35
0
0
5.5
0
-51.75
-2.25
0
-5.75
1.25
0
0
0
-0.25
0
-2
-0.25
-2.75
-16
0
-0.5
0
-1.5
0
0
0
-0.25
0
-24.25
-9
-2.25
-2.25
0
0
-0.25
-2
-1.5
-4.75
0
0
25
-0.5
0
0
-0.25
-0.5
0
-2.25
12.25
0
-0.25
0
0
-5.25
0
-0.5
-9.5
5.25
0
0
0
0
-1.5
-1.5
-0.25
0
0
0
12.25
0
0
0
-0.5
0
-0.5
-4.75
0
0
0
0
-0.25
7.25
-0.5
34.5
0
2.25
-0.5
0
0
-0.5
-0.5
0
0
0
22.75
0
0.75
0
-0.5
0
-0.5
2.25
-0.25
0
0
0
2.5
1
0
0
0
4.5
-0.25
0
0
0
-2.5
0
-4.25
-0.25
0
0
-0.5
0
0
-0.25
-0.25
0.75
0
4.75
0
0.75
-7.75
0
0
0
0
2.25
12.25
5.25
-0.25
-1.75
0
0
-0.5
0
-0.5
0
-0.5
-0.5
0
1.25
1.25
0
0.75
-0.25
0
-0.5
0
-0.25
0
4
1.5
0
0
3
0
0
0
0
0
-0.25
-0.5
4
-0.25
-0.25
0.75
1.25
-0.25
-0.5
-0.5
0
-0.25
-0.5
0
-1.75
4.5
0.75
0
0
-1.75
-3.75
-11.75
0
-0.5
-0.5
0
1
-0.5
-0.5
0
0
3.5
-0.25
0
-0.5
-0.5
2.5
-2
0
0
0
0
0
0
-0.25
0
21.25
-0.5
0
0
0
0
0
0
-0.25
-6.5
0
-0.25
-0.25
-0.5
-0.5
0
3.25
0.75
0
0
0
0
0
1.25
-2.5
2
0
-0.25
-0.25
-0.25
0
-0.5
-0.5
0
2
0
-7
0
11
0
52.25
0
9
0
-6
3.75
0
0
2.25
-8
-0.25
1
0
0
10.75
0
0
0
0
-0.25
0
-2.75
0
7
-0.5
-1.75
-0.5
-5.5
-3
0
1.5
-0.25
3.25
-2.5
-0.5
44.75
0
0
0
-4.25
3
-2.5
-5.5
15.25
9.25
-0.5
0
0
0
0
-74.5
5.5
6.25
0
0
5.5
-0.25
0
0
-0.5
-1.5
-0.25
0
-0.5
0
-0.5
0
13
0
0
46.5
0
-0.25
-0.25
0
0
3.5
0
-19.5
0
-9.75
2
90
88
-0.5
0
0
0
-1.75
0
29
0
0
6.25
-11.75
-1.75
-1.75
-0.25
0
0
-0.5
-0.5
-0.25
-9.25
0
0
15.25
0
-0.25
0
0
-0.25
-0.25
-2
-1.5
-35.75
-1.5
0
5
-19.75
0
0
3.5
7.5
-0.5
-0.5
23
-7.5
0
-0.5
-4.25
-12.25
-27
0
3
-8.5
-3.5
-0.5
-0.25
52
-33
10.25
-17.25
0
4.5
0
0
25.25
1.5
0
2.5
-0.25
0
3.5
0
-0.25
0
-0.25
-1
-48
45
-7.25
0
-0.5
0
0
-0.25
0
-5.75
1
0
0
0
-2.5
7.75
-0.25
1
0
-0.5
-0.25
-6.5
0
-0.5
4
12
0
-4.25
0
-1.75
-2
-2.75
-8.5
-0.5
-13.75
4
0
0
-0.25
5.5
0
-0.5
-0.25
0
-0.25
4
-6.5
-0.5
-0.5
0
-4.25
1.5
0
0
1.5
1
-3.5
0
0
0
-3.5
0
-0.25
1.5
-0.25
-0.25
1.5
-1.5
0.25
1
1
0
-0.25
0
0
-0.25
-1.5
0
-0.25
0
-0.5
0
148.25
6.5
0.25
0
0
-0.25
-0.25
-0.5
-0.5
-0.25
0
0
-15.5
-2.5
0
0
-0.25
-47.5
0
-0.5
-1.75
0
-0.25
-1.5
7.25
0
-0.25
-57.5
0
0
-1.75
-3
5.5
-0.25
-0.5
0
-60.25
-10.5
0
-9.25
0
-0.25
91.5
0
-0.25
-1.5
-0.25
-0.5
0
0
0.75
-2.5
4.75
0
0
0
-1.5
-0.25
0
0
8.25
0
-28.5
0
-0.5
-14.5
0
-0.25
0
-0.25
-5.5
0
-0.25
9.5
0
0
3.5
0
3
-1
-1.75
0
-0.5
0
-0.25
0
-1.75
53.5
0
0
-1.75
-0.25
0
-1.75
0.5
0
0
-8
25.5
0
-8
0
-14
-0.25
-0.5
0
0
0
-0.25
-0.5
0
-0.5
0
0
-1.75
0
0
0
-2.25
25.25
0
-0.25
0
0
-0.5
-7.75
23.75
0
-3.25
-0.25
0
-10
-0.25
-0.5
0.75
-4.75
-2.5
0
-2.25
0
24.25
0
0
12
0
0
23
-2.25
96
31.75
-2.75
-0.25
-21.25
-0.5
39
-21
-5
-0.5
0
4
0
3.5
-29.25
0
3.5
-2.75
0
-65.5
0
-0.5
18.75
-0.25
0
0
-0.5
0
-1.75
0
-6.25
0
0
0
-0.25
11.75
0
-0.25
0
1.5
0.25
0
-19
0
0
0
0
5.5
-0.25
2
3
-0.5
-1
-12.5
-0.25
0
-7
-20.25
3.5
0
0
3.75
0
0
0
0
5.25
73
0
0
0
-0.25
22.25
11.5
-44.25
-6.25
0.75
2
-6
-5.5
0
0
0
1
-26
0
0
0
0
5
0
-0.25
-14.75
0
-0.5
-0.5
-0.25
-0.5
0
0
-6.25
-0.25
1.25
0
-0.5
0
1.5
-0.5
0
1.25
-0.25
0.25
0
-0.25
24.25
-0.5
0
-0.25
0
-1.75
0
0
-0.5
-0.25
-3.75
0
-0.5
0
0
0
-0.25
-2.5
11
0
-0.5
0
-0.5
3.5
2.5
-0.25
0
0
-1
0
-0.5
0
-1.75
0
-0.25
0
-0.5
2
-0.5
0
0
0
-7.75
6.5
0
0
0
0
-0.5
0
0
6.5
3.5
0
0.5
6
-0.25
28.5
0
0
7.5
-4.25
-5.75
0
-0.25
-1.75
6.5
0
12.25
-0.5
0
0
-0.25
35.25
0
0
-1.75
36.25
-0.25
-43
0
12.5
5.5
0
0
-2.5
-0.25
0
-0.25
1.5
-2.75
0
-0.5
0
0
0
0.5
0
75.5
0
-2.5
2.5
-1.75
15.25
2
-0.25
-0.25
0
-0.5
2.5
0
2
0
0
-0.25
0
16.5
0
-0.5
-0.25
0
-3.25
-1.5
-3
4.5
-0.5
-0.25
-0.5
-37.25
-12.25
0
-2
-0.25
-0.5
0
0
4.5
0
-0.5
12.5
-3.5
0
0
-0.25
-0.25
0
4.5
-0.5
0
0
24
0
0
0
0
-0.25
0
-0.25
-8
-2.75
-4
2
0.75
-0.25
-0.5
0
-0.5
-4
0
0
0
0
0
13.5
0
0
0
-0.25
0
-0.25
0
-0.5
-18.5
0
-0.25
0
28.75
0
-12.5
0
0
-9.75
0
0
-0.5
-0.25
0
0
-6.25
0
-0.25
-2.25
-0.25
-0.5
-0.5
-0.5
3
-7.75
139.25
-4.25
7
0
0
0
-24
0
-6
-2.75
-0.25
-0.5
3.5
-26
-1.75
-3
0
0
-10.5
0
0
0
0
0
0
0
14.25
4.5
0
-0.5
-4
0
0
0
0
-0.25
-3.5
0
-0.5
-0.5
0
0
0
0
31.25
0
4
6.75
-3.75
0
-0.5
0
-2.5
0
5
-3
0
0
0
3
-0.5
0
41.25
-0.25
0
64.25
-0.5
-10.25
-2
-8.25
-0.25
0
0
-0.5
-0.5
0
0
-6
3
-6
-1.75
-0.25
-16.75
0
3.5
12.75
0
0
-0.5
-4.75
0
-0.5
-0.5
0
0
4.5
-2
-2.25
-2.75
3
-6.5
-7.75
-0.25
0.75
-1.75
-0.5
-0.25
1.5
-42
4
0
0
0
0
0
0
-0.25
0
0
0
1.5
0
-0.25
2.25
-9.25
0
13.25
-0.25
-1.5
-0.5
3.5
-0.5
0
0
0
7.75
0
0
-2.25
0
0
22.25
0
0
-9
-0.25
-0.25
-0.25
-0.5
5
-0.5
-2.5
1.5
5.5
-7.75
-0.25
-0.5
-3.75
0
0
0
-0.25
-4
0
0
54.75
0
0
4
-6.25
-9
0
-2.5
-6
8
-0.25
5.25
-2.5
0
0
-0.5
0
0
0
0
0
11.75
0
26.75
0
-0.5
-40.75
0
-73.75
14.75
-2
0
10.75
-0.25
-8.25
-0.5
0
-7
0
-2.25
-2.5
-16.75
-2.25
36.25
-5.75
-4
0
0
-0.5
31
-3.5
-0.25
0
-12.75
1.5
-4.5
-0.5
0
-0.5
5.25
0
0
0
-0.25
-1.75
-1.75
0
11.25
-5.25
0
-14.75
-0.5
-19.25
0
-0.5
-6.25
-0.25
0
-8.25
0
-0.5
0
-0.25
0
0
0
-0.5
0
0
0
41.75
-0.25
0
0
-0.5
-0.5
-1
-27.75
-2.25
-0.25
0
0
0
-0.5
-4
-7.75
-12.75
-0.5
0
0
0
0
19.25
0
0
0
0
0
0
-0.5
-0.25
-0.25
0
-0.5
1
-14
0
4.5
11
0
0
0
-0.5
42
0
0
-8.5
-32.5
-0.25
-7
-0.5
6.5
-2.5
-0.5
-0.5
-6.25
0
17.5
0
-7.5
0
0
-0.25
0
-3
0
-4
-0.25
-0.5
-6.5
-20.75
-0.5
0
0
25
0
0
15
0
0
-2.5
0
0
-0.25
10
1
0
0
-0.5
1
0
-4.75
0
-2.25
0
9.75
0
-0.25
-0.5
-4.75
4.5
0
0
0
-13
0
0
-1.75
-4
7
4
-0.5
-0.5
-0.5
-2.25
3
4.5
0
2
0
-0.25
3
-9.25
0
0
-0.25
-0.5
-0.25
-2.25
-2
-3
0
-0.25
-1.5
4.75
0
0
0
0
-1
0
-0.5
-0.25
-0.25
7
3.5
-8
-5
0
-0.25
0.5
-0.5
0
0
4
0
-0.25
-2.25
3.5
-3
1.75
0.25
3.5
0
-0.5
0
0
-0.25
0
-9
18.75
-1.75
-7.5
-0.5
22.5
3.5
0
1.25
-4.75
-7.5
-3
0
4
0
0
-0.5
0
-0.25
6.75
0
-0.5
0.75
3
0
0
55.75
3.5
0.75
-0.25
-5.5
-0.5
-0.5
-0.25
-0.25
0
-0.5
1.5
0
-4.75
0
0
3.5
25.75
53
0
0
0
0
-11.25
0
-5.75
0
-0.25
-0.25
0
5.5
-2.75
0
-1.75
5.75
0
0
0
-7.5
-32.5
0
0
-0.5
0
0
2
0
-2.25
-0.25
0
-0.5
-0.5
0
13.25
-0.5
0
-0.5
1.25
1.5
0
0
0
0
-19.5
-0.25
-2.5
0
14.25
8
3.75
0
0
0
-0.5
-0.25
-0.25
-2.25
7
0
0
0
-0.5
-2.25
0
4.75
-5.5
0.75
9.5
-0.25
0
26.75
0
-0.5
-0.5
-0.25
-1.75
1
-0.5
-5.25
0
-4.75
0
0
-0.25
0
0
-0.25
-17
-0.5
3.5
6.5
-1.75
-0.5
2.5
0
0.75
4.25
5.75
3
-1.5
-0.25
1.5
0
-4.5
-0.25
-0.5
-4.5
-8.25
-13.5
-2.25
0.75
8
-88
0
-0.25
-18.5
-0.5
13
-3.5
0
-0.5
-0.5
-15.5
2.5
0
0.5
0
-1.75
-0.5
-2.25
0
5.75
-0.5
-17
8.25
-1.5
0
-0.25
1.5
-14.25
0
5
13.25
0
-1.75
54.25
0
10
-0.5
-6.25
0
0
-0.25
-2
0
-0.5
11
-8.5
52
0
0.5
0
0
-0.25
0
0
0
-0.5
0
0
-0.25
8.75
3.75
11
-33.25
-3.75
-4
0
0
3
0
1
0
15.5
0
-2.5
-0.25
0
0
-0.25
-2.5
11
7
0
-0.25
4
1.25
0
-0.25
0
-0.5
2.25
4.5
8
-1.75
0
6.25
0
1.5
0
4
0
-4.75
0
-0.25
0
-0.5
-0.25
-0.5
34.75
0
1
-0.5
0
-0.25
3.75
0
20
-0.5
0
0
0
-7
0
0
-8.5
0
0
8.25
27.75
-0.25
0
-3.25
-6.75
0
1
-13.5
0
-1
-0.25
-0.5
1.5
-0.5
0
0
0
1.25
0
0
0
-0.25
0
0
2
-2.25
-7.75
-6.25
-21.25
0
0
0
-1
-10.25
-0.25
4.5
0
-5.25
-0.25
-3
0
26
7
2.25
-18.25
0
0
-0.25
-0.5
-1
1.5
-4.75
-0.5
-0.25
0
0
-17.25
0
-0.25
-0.5
0
0
4
-4.75
0
0
-0.5
-0.25
0
4
6.25
-1.5
-0.25
0
-1.5
-1.75
0.75
-19.25
29.5
0
0
11.75
14
0
0
0
-0.25
-0.25
-2.25
0
-0.5
9
2.5
0
0
0
2.75
-0.25
0
0
6
-2.5
3
0
0
0
-0.25
0
0
0
13.25
-0.5
-0.25
7
0
-0.5
-0.5
5.75
0
0
0.75
-0.5
4.5
-0.25
0
6
-5.75
1
-2.25
-0.5
0
0
-8.5
-16.75
1.25
0
-2.75
-11.75
-0.25
0
-0.25
-8.75
0
-2.75
-0.5
41.75
-7.25
-0.25
-0.25
0
-0.5
5.25
0
-0.5
0
-0.25
0
13.25
0
-0.5
-24.5
-1.75
-0.25
-28.25
-0.5
-0.5
0
-44.25
0
0
0
24
0
14.5
-0.25
0
-1.75
9
-16.75
-4.25
0
-2.5
0
-3.75
-0.5
-11.75
0
-0.5
11.25
0
6.5
5
0
0
0
-0.25
-2.25
50
-0.25
0.75
-0.5
-0.25
14
-1.75
15.5
0
-0.5
0
35.5
0
0
-2.25
17.25
6.25
0
-2.25
0
-7.5
1.5
0
1
0
0
-6.5
0
0
-8
-9
5.25
-0.5
-4
-5.25
0
3
0
0
-0.25
-50.25
-2.75
-2
-5.5
-4
-0.25
0
-1.75
-1.5
6.25
0
-0.25
-0.25
0
5.25
-0.5
-20.5
0
0
0
0
0
0
-15
0
0
2.5
0
-0.25
-0.5
-0.5
0
-10
0
0
-0.25
2.5
9.25
0
0
1.5
0
-2
-5.5
5.75
-0.5
0
0
-2.25
-4.75
0
0
1.5
0
-7.5
0
0
2.25
9
6.5
-1.75
5.5
-0.25
-2.5
7.75
-1.75
3
0
0
6.75
0
-0.5
-52
3.5
-2.25
0
8.75
-1
-1.75
0
-0.25
0
0
7
-7.75
0
60.25
48.5
-2
-2.25
-11.25
0
0
-3
0
-0.25
-0.5
-2.25
-1.75
0
0
25.75
0
0
-0.5
0
0
-0.25
2
25.5
-0.25
0
3.25
-4
-0.5
0
0
0
-2
0
0
3.75
0
4.75
0
4.25
9.5
-0.5
-3
-0.25
-6.5
0
-0.5
-0.5
0
-0.5
-1.75
0
0
9
0
0
-0.25
0
0
-0.25
-0.5
-5.75
0
-1.5
-4.25
0
-2.75
-1.75
0
0
-26.75
-0.25
-0.25
-22
-0.5
0
-0.5
-0.5
0
13.25
11.5
3.5
23.5
3
0
-0.25
-0.5
0
-0.5
-4.75
0
0
11.25
-7.75
-0.25
-0.5
0
-0.5
0
0
0
-2.25
5.25
1.5
-2.5
0
-0.25
-1.5
0
-1
0
3.5
6.5
-12.25
-0.25
4.5
0
-6
0
7
0.5
0
1.5
-30
0
-6.75
-0.25
-0.25
0
-3.75
-0.25
-0.5
0
0
9
-39.75
0
0
-5.75
-0.25
0
4
0
16.75
-0.5
-0.5
-0.25
-1.75
0
0
29
-1.75
0
0
5
-7.25
-0.5
0
-7
-2.5
-5.75
9.5
3.25
-0.5
-2
6.5
0
-1
0
3
0
-0.25
0
0
-0.5
0
0
-26.25
0
-1.75
0
-0.25
-0.25
0
-12.25
0
-0.5
-0.5
-0.5
0
0
0
-1.75
0
0
0
-0.25
41.75
-0.5
16.5
-11.75
0
-1.75
-0.25
-53
-1.75
0
-3
0
4
0
0
-0.25
3.75
4
0
0
-0.5
0
-0.25
0
0
-0.5
3.75
0
4
2.25
0
0
-1.75
0
-0.25
0
-7.25
-15.75
0
18.25
0
-1.75
0
-1.75
-0.25
-0.25
-0.5
0
0
-0.5
1.75
-0.25
15
0
0
-0.5
5.25
0
0
0
13.75
10.75
5.25
-3
-5.75
0
0
-0.25
-2.5
-0.25
0
-0.5
-0.25
-0.5
-0.5
-0.5
-1.5
0
0.75
0
0
0
0
0
0
0
0
0
-2.25
3.5
-0.25
10.5
0
-6.5
0
-2
0
0
-0.25
-0.25
0
-1.75
0
-0.5
3.5
0.75
95.25
-0.25
-0.25
0
4
-4.75
-0.25
21.25
0
0
-3
5
0
0
0
0.75
0
0
0
0
-11.5
0
-6
0
-0.25
0
-3.25
-1.5
0
-0.25
-0.25
3.75
-0.5
1.25
-0.5
-0.5
0
4
0
-0.5
4.25
0
0
-9
-5.75
-0.5
0
37
10.5
0
1.75
-0.5
-0.25
-0.25
-8.25
2
0.75
-0.25
-5.75
0.25
-0.5
-29.5
-4.75
0
0
0
0
0
0.5
-1.5
0
1
-0.5
0
-0.25
0
0.75
0
-0.5
-0.25
0
0
8.75
34.75
0
-0.5
0
-11.75
20.5
-0.5
-9.75
-0.25
0
-0.25
-2.25
-2
-3
-2.25
0
0
-54.25
0
0
5.5
0
0
0
0
-2.25
0
-0.5
0
-0.5
0
49.5
0
0
0
-0.25
0
0
-0.5
0
9.75
0
0
0
-1.75
-0.25
10.75
-0.25
0
-0.5
4
0
13
0
-0.5
-0.25
-4
-0.25
-0.5
18
-0.5
0
0
46.75
0
4.5
-1.75
-3.5
0
-0.5
-0.25
-0.25
-2.75
-0.5
-55.75
-0.5
0
-4.25
-20.75
0
-8.5
-3.25
0
-0.5
0
-0.25
-1.75
-2.25
49.5
0
-37
-0.5
-12.5
-2.5
-15
-2.25
0
-21.5
-0.25
0
-7.75
-1.75
7.5
0
-1.75
-15.25
0
0
0
10.75
0
-0.25
0
0
-0.5
-0.25
-0.5
26
-8.5
0
-0.5
-0.5
0
0
0
10.75
-1.75
0
-2.25
17
-33
24.5
-0.5
0
8.5
2.5
-4
0
-4.5
0
-21.5
0
-0.25
7
-0.25
-11
-0.25
-0.5
-4.5
7.5
5.25
0
-0.5
0
3.75
9.75
0
0
0
-7
-0.25
0
-15.5
2.5
-0.5
0
0.5
-0.25
0
0
-0.5
-0.5
2.25
0.75
-0.25
-0.25
-3
-0.25
9.5
-1.5
-6.75
-4.5
0
-0.5
-0.5
0
0
-26.25
20.25
20.75
0
-0.25
0
6
0
-1
0
5
-0.25
4
14.5
-67.25
-0.5
-0.5
-0.5
-0.5
-0.5
0
0
-2.5
0
-21
-3
6.25
3.5
-8
0
-2.5
0
-1.75
51.5
1.25
-0.25
-0.25
0
0
14
-0.25
0
-47
-1.5
31
-0.5
-0.5
-58.75
-5.75
2.5
-50
0
0
-16.25
0
-0.25
21.5
8
-0.5
-0.25
0
-3.25
0
-0.25
-0.5
1
-4.5
0.75
-4.25
0
0
-0.5
-0.5
-1.5
0
1
-2
-2
0
1.25
0
-0.25
-1.75
25.75
64.25
-2
-2.75
0
0
0
0
-0.25
0
3
0
0
-0.5
13.5
-0.5
-0.5
0
-2.5
-0.25
0
0
3
0
0
0
0
-0.25
26.75
9.5
12
-2
-0.25
-0.5
-0.5
4.5
0
0
0
-1.75
-6.25
0
-0.5
-2.75
4
0
0
-0.5
-0.25
0
12.25
-0.5
4
0.25
11.5
-1
18.25
0
21.5
0
0
-11.5
0
0
0
5.25
0
0
-4.25
46.5
0
-7.5
0
-2.5
-0.5
-8
2.5
0.5
-0.25
0
0
5.25
0
-6.25
-10.5
5.75
-5.5
0
0
-0.25
-0.5
0
-0.5
4
0
-3
-1.75
0
0
4
3.5
-2.25
0
-0.25
-0.25
-10.75
0
0
-0.5
0
-0.5
7
-2.5
-6
-1.75
120.75
0
2
3.5
-7.75
-10.25
0
-14.25
-0.25
-14.5
-3
4
-0.25
17.75
0.75
0
-2.75
4.5
-1.75
8.5
0
-3.5
0
-1.5
5.75
3
0
-1.5
0.75
0.75
0
0
-0.25
0
6.5
0
5.5
-0.5
0
0
-0.5
0
0
12.5
0
3
0
0
0
-0.5
0
0
0
0
-5
25
-1.5
-0.25
0
-1.5
8.25
-8.75
46.25
0
-3.75
-0.5
42.5
0
-8.5
0
0
3.75
0
-17
-2.25
-10.25
0
-3
0
0
0
-1
-0.5
0
0
4
-2.5
0
9.5
-5.5
-4.75
7
-2
0
4.5
0
0
0
-10.25
1.5
6.75
-0.5
0
0
0
26.75
38.5
0
3.5
-4.5
-0.5
-0.5
5.5
0
-2.5
-0.5
6.75
-0.5
-5.75
0
3.5
0
0
-0.5
-0.25
-0.25
-8.75
-3.5
2
0.75
-2
33
36.25
-7.5
1.5
7.25
0
-0.25
0
0
4.5
-0.25
-4.5
11.5
-0.25
-3
0
-22.75
-1.75
-4.25
0
0
2.25
0
1.5
-4.75
-0.25
-2
-2
0
-13.5
0.5
-10.25
5
5.5
0
0
0
0
-0.25
2.5
0
-0.25
2.5
0.75
0.75
-0.5
-7.5
50.75
-0.25
2
-17.25
4
-0.5
0.75
3
11.25
4.5
0
0
-1
-0.5
-11.25
-25
2
3
4
-1.5
0
0
-0.5
1
0
-8.25
0
-38
0.75
0
0
0
-2.25
3.5
0
-10
-0.5
-1.75
9.75
1.5
3
0
-5.75
9.75
0
5.5
0
0
0
11.25
-28.5
20.5
0
0
-0.5
2.5
-2
0.5
-0.25
-9
-0.5
2
0
-0.5
0
0
2.25
0
0
0
0
-7.75
0
-7.75
0
12.5
-0.25
-0.5
0
24.5
-0.25
0
-0.25
0
0
-4.75
-0.5
0
0
0
2
0.25
0.75
21.25
0
0
0
0
0
19.25
96
0
-0.5
-0.5
-0.5
-0.25
2
10.5
0
3.5
0
0
3.5
0.75
-46
-0.5
5.25
-2.5
-2.5
-4.75
-0.5
-0.25
-0.5
0
-2
0
0
0
0
-2
0
10.5
-5.75
-3
-2.25
7.75
-0.25
-0.25
1.5
-0.25
20.25
-23
-0.5
0
0
0
0
3
0
-0.5
-2.25
19.75
6
1.5
0
-0.25
0
1
0
-0.25
-0.5
0
0
-0.25
-6.5
-1.75
-1.25
-2.5
0
0.5
-63
0
4
0.75
-0.25
0
0
0
-0.5
0
0
0
-0.5
-5.5
0
13
-2
0
-0.25
7
0
-0.5
-0.25
0
-6.5
0
0
0
0
0
-48.5
-1
-0.25
-0.5
-0.5
-8.5
0
1.75
0
0.25
-6.25
0
-1.75
0
-2.25
2
3.5
-2.5
2.5
-6.5
0
0.25
0.5
21.75
1.5
-9.5
-3
0
-44.5
0
-0.25
4.5
-2
-3
0
-1.75
0
0
-11.25
0
-72
-0.5
0
0
-4
-13
0
-14.25
-0.25
1
-3
-2.25
14.75
11.25
0
0
0
0
-2.5
3
81.75
-1
0
-0.25
-0.25
-0.5
-0.5
0
-4
8.5
4
8.5
0
0
1.75
0
0
-1
2
0
0
-0.25
0
3
0
0
0
-2.5
-5.5
0
-0.5
-0.25
0
-1
0
1
-0.25
5.25
-0.5
0
0
92.25
-8
0
-3.75
-5.5
-0.25
-0.25
0
-2.5
0
-0.25
-0.5
-3
-0.25
-0.5
1.5
-0.5
0
56.25
0
-0.25
0
6.5
-1.5
0
-4.75
-3.25
-0.25
-0.25
0
0
50.25
-0.5
6.75
-17.25
1.25
-0.25
0
-3.5
-0.5
0
-3.5
-2.25
0
-8.25
0
0
0
0
0
-2.25
-6.5
-7.75
-5.75
-2
0
0
-0.25
-59.25
-8
-0.25
5.25
-0.5
0
-0.5
-1.75
48.75
15.25
-5.75
0
-0.5
26.25
-4.25
0
0
-9.75
0
6.25
0
0
-1.5
-4.5
0
2
-0.25
-0.25
-0.5
-0.5
8.5
0
-0.25
0
-13.25
-1.75
-6.75
0
0
26.5
-0.25
-1.75
-0.5
0
-1.75
-29.25
0
0.75
-11.75
-10
0
-1.5
0
-0.5
1.5
-0.25
-0.25
-0.5
2.5
1
-0.5
0
4
0
0
0
7.75
0
9
0
0
0
4
-0.25
18.5
-0.25
-0.25
-1.75
24.5
-2
2.25
-1.5
-1.75
0
-0.5
-1
0
0
0
22.25
-3.5
-2.75
-0.25
1.75
-71
-0.25
-0.25
-2
0
0
-1.75
-0.5
0
0
22.75
-8.25
0
18.5
-1.75
-2.5
0
0
4.5
-9.75
3.75
0
-0.25
0
-0.5
0
0
0
-16
-0.25
-0.5
0
-52
-0.5
0
-0.5
2
0
0
24
-1.75
2
0
1.5
0
-0.25
0
0
-0.5
0
-0.5
-1.75
0
-1.5
-1.5
0
-8
0
0
-0.25
13
1.25
0
0
-0.5
1
1.5
0
-0.5
-0.5
-2.25
-2
6.5
7
-0.5
-1.75
-0.25
-6.75
0
-0.5
0
0
0
0
0
-0.5
38.5
-2.25
-1
0
-0.25
2.5
-5.75
-3.25
6
1.5
4.5
0
0
-11.25
0
-6.75
-0.5
0
-0.25
0
70
-12.5
6.5
-0.5
1.5
0
37.5
0
0
-0.5
-0.5
0
5.5
0
-0.25
-0.5
-0.5
-17.5
-3.5
-0.5
-0.5
0
1.5
0
0
-0.5
2.5
0
-0.25
-17.75
-2.75
-0.5
-0.5
5.25
-0.25
0
-16.5
16.75
0
0
-1.75
-2
26.5
-0.5
5.5
-0.5
-0.25
11.75
0
0
1.5
-0.25
1
-1.75
0
0
0
0
4
0
0
9.75
-0.5
-0.5
147.75
2
2
-0.5
2
-0.5
2.25
-0.25
0
-0.5
0.75
0
0
-1.75
-0.5
0
-7.25
-0.5
0
-9.25
0
-0.5
0
7.5
-18.5
0
-2.25
-0.5
-0.5
18.25
-18
-5.5
6
-53.5
-0.5
8.75
0
0
4
-4.75
0
-0.5
0
5.75
-0.25
-5.75
0.75
2.5
0
0
0
-1
-3.25
-5.25
0
-1.75
-0.25
0
-0.25
-0.5
-0.25
-13.75
-6.5
0
1.5
4
-10.5
0
-0.5
0
0
-0.5
10.5
-0.5
0
0
-4.75
-0.25
0
0
-7.25
0
5.5
0
2
0
0.5
2
-0.25
0
-0.5
-0.5
35.5
0
-0.5
-8
15
4.75
0
-0.5
-0.25
-0.5
-41.25
0
-6.25
0
-2
0
-0.25
0
-2.5
-0.5
0
0
0
-0.25
0
-4.25
-0.5
-1.75
-0.5
0
-4
0
1.5
0
-1.75
-0.25
0
0
-2
-0.25
0
0
0
-0.25
0
-45.25
-0.5
-0.5
0
0
0
-1.5
0
55.75
-0.5
0
7.25
-0.25
0
-15
-0.5
0
0
-0.25
15.5
0
0
-0.5
-0.5
-2.25
0
0
-6.75
0
-0.25
0
-0.25
0
0
4
0
-1.5
0
0
-0.25
0
0
-0.25
5.25
-0.25
-15.75
0
-1.75
-4.5
-5.5
0
0
0
-17.75
0
35.25
-0.5
-14.75
-0.25
8.75
0
0
0
3.5
-1.75
-0.25
0
-0.5
0
-0.5
0
0
0
18
35.75
0
3
0
-0.5
-0.25
0
0
-0.5
-0.5
95.75
-0.25
0
-0.5
-0.5
0
-5.25
-7.25
0
0
0
-2.75
0
-1
-1.75
0.25
0
-1.5
-0.5
0
-0.25
23.5
151.5
-0.5
2
-0.25
0
0
-0.5
-1.75
30.5
2.5
-1.5
0
0
0
-0.5
-21.5
0
6.5
0
0
-4.75
0
0
-0.5
-0.5
0
-0.25
21.25
-0.5
-0.5
6.75
-3.25
5.25
0
0
0
1.75
-1.5
-0.5
-0.5
-2
-6.5
-1.75
3.5
-1.75
4
4.75
0
0
0
4.75
1.25
0
-0.25
16.25
1.5
-4.25
0
4.5
0
0
-53
-1.75
-7.25
-2
-2.75
-0.25
1
0
0.5
-0.25
0
0
-2.25
-0.5
-0.25
5.25
0
0
-1.75
0
-0.25
-46
0
-2
-1.75
0
0
-2.5
0
2
-0.5
-0.25
0
-13
-3.75
-1.5
0
-2.5
-6
0
-5.25
-12
2
0
0
0
-31.25
0
-2.5
0
-0.5
-6.75
-0.5
-0.25
-4.25
-0.5
0
7
0
0
0
-0.25
0
14.75
-0.5
-0.25
0
0
-1.75
-0.5
-0.5
0
-1
0
0
3.5
0
0
-0.5
-2.25
0.25
-7.75
-0.5
-0.25
-1.75
3.75
4
4.5
0
-4.75
-2.25
-2.5
-8.75
0
-0.25
-8.5
0
-7.75
-22
-6.5
2.5
0
0
0
-0.5
0
0
0
0
7.5
0
-1.75
-1
-0.5
-0.5
-0.5
0
30
-2
-0.25
0
0
-2.25
-0.5
-1.75
0
0
-0.25
-0.5
6.75
-0.25
-2.5
-0.5
-32.5
39.75
0
0
-51.25
0
-17
-16.5
-0.5
-2.75
0
-0.25
0
125
-0.25
0
-0.5
-1.75
1.5
0
-7.25
0
0
7.25
-0.5
-0.5
0
0
-7.75
-19.5
0
-2
0
0.5
0
-1.5
2.5
0
-1.75
-0.25
0
0
-0.5
-2
13.5
-0.5
-0.5
0
-5.5
-1.75
-2.5
-4.5
0
6
0
-0.25
-1.75
0.5
-0.25
-0.25
-1.5
0
8.5
-0.5
3.5
0
0
1.5
0
1
1.5
0
-0.25
0
0
20.25
21.75
-0.

[Noodles.]

Thank you for listing the whole list, I enjoyed reading it. I have chosen the following list (randomly!):
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
The method I used: (No Excel needed)
Throw dice. You now have a completely random number. Take the item from your list with that number, as many times as you want (Remember, the number was random!)

Try it out!

[Troll_Inc]

[ QUOTE ]
Thank you for listing the whole list, I enjoyed reading it. I have chosen the following list (randomly!):
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
The method I used: (No Excel needed)
Throw dice. You now have a completely random number. Take the item from your list with that number, as many times as you want (Remember, the number was random!)

Try it out!

[/ QUOTE ]


This won't work. There are more than 12 numbers.

I would like to do something like 30 samples at 50,000 numbers each.

[_dave_]

It would probably be easier to pull them from the database directly - or you could use some of that WSH scripting to pick random cells from Excel.

There must be a way to do it from excel itself, probably with VBA - I don't know enough to tell you how to do it in that way.

Maybe xpost in CTH? - there are lurking excel gurus in there on occasion [img]/images/graemlins/smile.gif[/img]

[jukofyork]

[ QUOTE ]
It would probably be easier to pull them from the database directly - or you could use some of that WSH scripting to pick random cells from Excel.

There must be a way to do it from excel itself, probably with VBA - I don't know enough to tell you how to do it in that way.

Maybe xpost in CTH? - there are lurking excel gurus in there on occasion [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]
Create a new column of random numbers and sort using them, then pick however many you want from the top of the randomly sorted list.

To create the random column, just use "=Rand()" which will create reals in the range {0..1}, then double click the "magic" excel duplication thingy (not sure what it's called...).

Juk [img]/images/graemlins/smile.gif[/img]

[Troll_Inc]

[ QUOTE ]
[ QUOTE ]
It would probably be easier to pull them from the database directly - or you could use some of that WSH scripting to pick random cells from Excel.

There must be a way to do it from excel itself, probably with VBA - I don't know enough to tell you how to do it in that way.

Maybe xpost in CTH? - there are lurking excel gurus in there on occasion [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]
Create a new column of random numbers and sort using them, then pick however many you want from the top of the randomly sorted list.

To create the random column, just use "=Rand()" which will create reals in the range {0..1}, then double click the "magic" excel duplication thingy (not sure what it's called...).

Juk [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]

This is a clever idea, but if I understand it correctly, you will only pick each number just once?

This is more of a probability density exercise, which I wasn't clear about initially.

I would like a program to go into the list of numbers and select one value, copy it, and then pull it out.

Then repeat on the intact sample (not n-1).

Do a total of "a lot of times", like at least 10,000+.

Then repeat this whole process about 30-40 times.

Your method should do this, but the next question is how, in Excel, I can repeat this (not manually). My understanding is that For/Next, If/Then loops take a long time in Excel [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img]

[jukofyork]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
It would probably be easier to pull them from the database directly - or you could use some of that WSH scripting to pick random cells from Excel.

There must be a way to do it from excel itself, probably with VBA - I don't know enough to tell you how to do it in that way.

Maybe xpost in CTH? - there are lurking excel gurus in there on occasion [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]
Create a new column of random numbers and sort using them, then pick however many you want from the top of the randomly sorted list.

To create the random column, just use "=Rand()" which will create reals in the range {0..1}, then double click the "magic" excel duplication thingy (not sure what it's called...).

Juk [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]

This is a clever idea, but if I understand it correctly, you will only pick each number just once?

This is more of a probability density exercise, which I wasn't clear about initially.

I would like a program to go into the list of numbers and select one value, copy it, and then pull it out.

Then repeat on the intact sample (not n-1).

Do a total of "a lot of times", like at least 10,000+.

Then repeat this whole process about 30-40 times.

Your method should do this, but the next question is how, in Excel, I can repeat this (not manually). My understanding is that For/Next, If/Then loops take a long time in Excel [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img]

[/ QUOTE ]
As sorry, I didn't realize you wanted to re-sample.

I think figuring this out in excel will end up such a pain that just writing a small program which takes a text/csv file as input and outputs another text/csv file with the re-sampled data might be easiest.

I think you can do sampling with replacement from within excel though:

1) You need to first install the "Analysis Tool Pack" which comes with excel - see here: http://www.cpearson.com/excel/ATP.htm

2) Then you need to follow the instructions from here: http://bcs.whfreeman.com/ips4e/suppl...cel/03_IPS.pdf

Sadly, I can't seem to find my MS-Office CD so can't test it myself, but I think it should work.

Juk [img]/images/graemlins/smile.gif[/img]

[Troll_Inc]

[ QUOTE ]

As sorry, I didn't realize you wanted to re-sample.

I think figuring this out in excel will end up such a pain that just writing a small program which takes a text/csv file as input and outputs another text/csv file with the re-sampled data might be easiest.


[/ QUOTE ]

No, my bad, I didn't explain it well.

What computer language would you recommend for writing such a program for someone who would have to learn the language?

p.s. I'll look at the Excel suggestion some more too.

[jukofyork]

[ QUOTE ]
[ QUOTE ]

As sorry, I didn't realize you wanted to re-sample.

I think figuring this out in excel will end up such a pain that just writing a small program which takes a text/csv file as input and outputs another text/csv file with the re-sampled data might be easiest.


[/ QUOTE ]

No, my bad, I didn't explain it well.

What computer language would you recommend for writing such a program for someone who would have to learn the language?

p.s. I'll look at the Excel suggestion some more too.

[/ QUOTE ]
In C/C++ it's about 30-50 lines of code and maybe 20-30 mins work at most. You might even be able to write it quite easily in an AHK script?

Give the excel method a try that I posted and if you can't get that to work I'll write you a small program to do what you want using ".csv" files tommorow...

Juk [img]/images/graemlins/smile.gif[/img]

[Troll_Inc]

OK, that .pdf totally worked.
A+++++


But I'd like to do this 30-40 times.
So I tried to make it a macro.
Write the results to column D (starting at cell D11).
Then insert a column so that it moves to the right and I can repeat.

This line is given as an error in my macro:
Application.Run "ATPVBAEN.XLA!Sample", ,ActiveSheet.Range("$D$11"), "R" _, 1000, True

I get Runtime Error 1004.
ATPVBAEN.XLA could no be found.

So it works onetime, but not in a macro...oh well beggars can't be choosers!

***********************
Sub Sampling1()
'
' Sampling1 Macro
' Macro recorded 10/30/2007 by wks46
'
' Keyboard Shortcut: Ctrl+s
'
Application.Run "ATPVBAEN.XLA!Sample", , ActiveSheet.Range("$D$11"), "R" _
, 1000, True
End Sub