*Dancing With The Stars*

It seems appropriate on this the first day our cowntdown hits single digits to wrap up the Dance Partners puzzler.

It would take too much computer time to answer the question "What's Hottie Hostess' partner's number if Hottie plus her invited guests total 1000?" (in the spirit of the 1000-point star problem) but here are all the solutions for dancer counts from 18 to 150.

(For the really technically interested, here's the source code of the program that solved this extremely interesting and non-trivial problem).

mollykew.tc

dancers

1-15 (16)
2-14 (16)
3-13 (16)
4-12 (16)
5-11 (16)
6-10 (16)
7-18 (25)
8-17 (25)
9-16 (25)

dancers

1-15 (16)
2-14 (16)
3-22 (25)
4-21 (25)
5-20 (25)
6-19 (25)
7-18 (25)
8-17 (25)
9-16 (25)
10-26 (36)
11-25 (36)
12-24 (36)
13-23 (36)

dancers

1-35 (36)
2-34 (36)
3-33 (36)
4-32 (36)
5-31 (36)
6-30 (36)
7-29 (36)
8-28 (36)
9-27 (36)
10-26 (36)
11-38 (49)
12-37 (49)
13-36 (49)
14-50 (64)
15-49 (64)
16-48 (64)
17-47 (64)
18-46 (64)
19-45 (64)
20-44 (64)
21-43 (64)
22-42 (64)
23-41 (64)
24-40 (64)
25-39 (64)

dancers

1-35 (36)
2-34 (36)
3-33 (36)
4-32 (36)
5-31 (36)
6-43 (49)
7-42 (49)
8-41 (49)
9-40 (49)
10-39 (49)
11-38 (49)
12-37 (49)
13-36 (49)
14-50 (64)
15-49 (64)
16-48 (64)
17-47 (64)
18-46 (64)
19-45 (64)
20-44 (64)
21-60 (81)
22-59 (81)
23-58 (81)
24-57 (81)
25-56 (81)
26-55 (81)
27-54 (81)
28-53 (81)
29-52 (81)
30-51 (81)

dancers

1-48 (49)
2-47 (49)
3-46 (49)
4-45 (49)
5-44 (49)
6-43 (49)
7-42 (49)
8-41 (49)
9-40 (49)
10-39 (49)
11-38 (49)
12-37 (49)
13-36 (49)
14-35 (49)
15-49 (64)
16-65 (81)
17-64 (81)
18-63 (81)
19-62 (81)
20-61 (81)
21-60 (81)
22-59 (81)
23-58 (81)
24-57 (81)
25-56 (81)
26-55 (81)
27-54 (81)
28-53 (81)
29-52 (81)
30-51 (81)
31-50 (81)
32-68 (100)
33-67 (100)
34-66 (100)

dancers

1-48 (49)
2-47 (49)
3-46 (49)
4-45 (49)
5-44 (49)
6-58 (64)
7-57 (64)
8-56 (64)
9-55 (64)
10-54 (64)
11-53 (64)
12-52 (64)
13-51 (64)
14-50 (64)
15-49 (64)
16-65 (81)
17-64 (81)
18-63 (81)
19-62 (81)
20-61 (81)
21-60 (81)
22-59 (81)
23-77 (100)
24-76 (100)
25-75 (100)
26-74 (100)
27-73 (100)
28-72 (100)
29-71 (100)
30-70 (100)
31-69 (100)
32-68 (100)
33-67 (100)
34-66 (100)
35-86 (121)
36-85 (121)
37-84 (121)
38-83 (121)
39-82 (121)
40-81 (121)
41-80 (121)
42-79 (121)
43-78 (121)

dancers

1-80 (81)
2-79 (81)
3-78 (81)
4-77 (81)
5-76 (81)
6-75 (81)
7-74 (81)
8-73 (81)
9-72 (81)
10-71 (81)
11-70 (81)
12-69 (81)
13-68 (81)
14-67 (81)
15-66 (81)
16-65 (81)
17-64 (81)
18-82 (100)
19-81 (100)
20-101 (121)
21-100 (121)
22-99 (121)
23-98 (121)
24-97 (121)
25-96 (121)
26-95 (121)
27-94 (121)
28-93 (121)
29-92 (121)
30-91 (121)
31-90 (121)
32-89 (121)
33-88 (121)
34-87 (121)
35-86 (121)
36-85 (121)
37-84 (121)
38-83 (121)
39-105 (144)
40-104 (144)
41-103 (144)
42-102 (144)
43-126 (169)
44-125 (169)
45-124 (169)
46-123 (169)
47-122 (169)
48-121 (169)
49-120 (169)
50-119 (169)
51-118 (169)
52-117 (169)
53-116 (169)
54-115 (169)
55-114 (169)
56-113 (169)
57-112 (169)
58-111 (169)
59-110 (169)
60-109 (169)
61-108 (169)
62-107 (169)
63-106 (169)

dancers

1-80 (81)
2-79 (81)
3-78 (81)
4-77 (81)
5-76 (81)
6-75 (81)
7-74 (81)
8-73 (81)
9-72 (81)
10-71 (81)
11-70 (81)
12-88 (100)
13-87 (100)
14-86 (100)
15-85 (100)
16-84 (100)
17-83 (100)
18-82 (100)
19-81 (100)
20-101 (121)
21-100 (121)
22-99 (121)
23-98 (121)
24-97 (121)
25-96 (121)
26-95 (121)
27-94 (121)
28-93 (121)
29-92 (121)
30-91 (121)
31-90 (121)
32-89 (121)
33-111 (144)
34-110 (144)
35-109 (144)
36-108 (144)
37-107 (144)
38-106 (144)
39-105 (144)
40-104 (144)
41-103 (144)
42-102 (144)
43-126 (169)
44-125 (169)
45-124 (169)
46-123 (169)
47-122 (169)
48-121 (169)
49-120 (169)
50-119 (169)
51-118 (169)
52-117 (169)
53-116 (169)
54-115 (169)
55-114 (169)
56-113 (169)
57-112 (169)
58-138 (196)
59-137 (196)
60-136 (196)
61-135 (196)
62-134 (196)
63-133 (196)
64-132 (196)
65-131 (196)
66-130 (196)
67-129 (196)
68-128 (196)
69-127 (196)