College Basketball Sectionals Page


Jeff Sagarin'stm College Basketball Sectionals Page



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This is a very difficult math problem to get the ultimate "perfect" answer - that is, the absolute
minimum distance sum.  The technique used is "simulated annealing". I'll be continually running it and trying to improve the answer.

So check here every once in a while to see if it's been updated.

Last updated: 2020 September 12 Saturday  06:17:32.136  Central Standard Time  = GMT/UTC-06:00
              2020 September 12 Saturday  12:17:32.136  Greenwich Mean Time    = GMT/UTC
JULIAN DATE= 2459105

College Basketball Sectionals


The 1-64 listing of the sectionals is in a rough east-west order. The combining of the sectionals into regionals will be done in the next stage. So don't read anything into the 1-64 ordering now. The goal is to minimize the total mileage - that is, have the teams as close together as possible. Actually, to minimize the product of the average distance times the root-mean-square distance. By mileage, I'm referring to the sum of the mileages from the 64 sectionals. The mileage for a given sectional is the sum of the distances between all possible pairs of teams in a sectional. In a 5-team sectional (which 33 are),there are 5*4 / 2 = 10 possible pairs of teams. In a 6-team sectional (which 31 are) there are 6*5 / 2 = 15 possible pairs of teams. 27 sectionals with 5 teams = 135 teams 27 * 10 = 270 pairs 37 sectionals with 6 teams = 222 teams 37 * 15 = 555 pairs ------------- ----------- 357 teams 825 pairs And the numbers to the left of each team's name are simply the code numbers used by the program for each team. They have no other significance. The suggestion here is that the host role of the sectionals would rotate among the teams so that each team gets to host its sectional every 5(6) years.
total golden miles=108510.3786 total pairs=825 average golden miles between pairs of teams=131.53 suggested T0=.368425019 total linear miles=72808.1405 total pairs=825 average linear miles between pairs of teams=88.25 suggested T0=.247205298 total miles squared=31700877.7303 total pairs=825 square root(mean miles squared) between pairs of teams=196.02 suggested T0=.549086104 ____________________________________________________________________________________________________ SECTIONAL# 1 total miles=213 average distance between teams=14 pairs=15 teams=6 7 Boston College 42.335653 -71.171165 $ 4 Boston U. 42.333987 -71.104774 $ 5 Harvard 42.378430 -71.116441 $ 6 Merrimack 42.667727 -71.119685 $ 3 Northeastern 42.339820 -71.087552 $ 8 UMass Lowell 42.655528 -71.324208 $ ____________________________________________________________________________________________________ SECTIONAL# 2 total miles=1478 average distance between teams=148 pairs=10 teams=5 15 Dartmouth 43.704793 -72.292591 $ 1 Maine 44.899236 -68.669199 $ 16 Massachusetts 42.388979 -72.528699 $ 2 New Hampshire 43.135641 -70.932837 $ 22 Vermont 44.477549 -73.193183 $ ____________________________________________________________________________________________________ SECTIONAL# 3 total miles=452 average distance between teams=30 pairs=15 teams=6 9 Brown 41.826211 -71.397556 $ 11 Bryant College 41.921264 -71.537983 $ 14 Connecticut 41.809265 -72.253690 $ 13 Holy Cross 42.238982 -71.807849 $ 10 Providence 41.843711 -71.437836 $ 12 Rhode Island 41.486212 -71.548116 $ ____________________________________________________________________________________________________ SECTIONAL# 4 total miles=423 average distance between teams=28 pairs=15 teams=6 24 Fairfield 41.160652 -73.257615 $ 25 Hofstra 40.714546 -73.600684 $ 19 Quinnipiac 41.418986 -72.894268 $ 23 Sacred Heart 41.221485 -73.241504 $ 21 Stony Brook-NY 40.917321 -73.124554 $ 20 Yale 41.311208 -72.926491 $ ____________________________________________________________________________________________________ SECTIONAL# 5 total miles=945 average distance between teams=63 pairs=15 teams=6 27 Albany-NY 42.660016 -73.771364 $ 34 Army 41.387872 -73.964306 $ 18 Cent. Connecticut State 41.690100 -72.768152 $ 17 Hartford 41.795655 -72.715094 $ 32 Marist 41.722038 -73.934304 $ 26 Siena 42.718412 -73.753731 $ ____________________________________________________________________________________________________ SECTIONAL# 6 total miles=139 average distance between teams=9 pairs=15 teams=6 33 Columbia 40.808990 -73.961249 $ 38 Fairleigh Dickinson 40.898432 -74.028195 $ 30 Fordham 40.861211 -73.885969 $ 28 Iona 40.925932 -73.787077 $ 31 Manhattan 40.889544 -73.901525 $ 29 St. John's 40.722047 -73.795134 $ ____________________________________________________________________________________________________ SECTIONAL# 7 total miles=124 average distance between teams=8 pairs=15 teams=6 35 Long Island U. 40.690000 -73.981667 $ 41 NJIT(New Jersey Tech) 40.742323 -74.178756 $ 39 Saint Peter's 40.727324 -74.071253 $ 42 Seton Hall 40.742601 -74.247369 $ 36 St. Francis-NY 40.693294 -73.991535 $ 40 Wagner 40.614548 -74.094308 $ ____________________________________________________________________________________________________ SECTIONAL# 8 total miles=552 average distance between teams=37 pairs=15 teams=6 50 Lafayette 40.698154 -75.207399 $ 53 Lehigh 40.606487 -75.380180 $ 37 Monmouth-NJ 40.278167 -74.006527 $ 44 Princeton 40.342885 -74.656825 $ 45 Rider 40.279275 -74.739327 $ 43 Rutgers 40.499549 -74.444319 $ ____________________________________________________________________________________________________ SECTIONAL# 9 total miles=88 average distance between teams=6 pairs=15 teams=6 48 Drexel 39.954002 -75.192957 $ 47 La Salle 40.038723 -75.154065 $ 49 Pennsylvania 39.950946 -75.193513 $ 51 Saint Joseph's 39.995371 -75.239062 $ 46 Temple 39.980946 -75.152955 $ 52 Villanova 40.038166 -75.344632 $ ____________________________________________________________________________________________________ SECTIONAL#10 total miles=655 average distance between teams=66 pairs=10 teams=5 57 Delaware 39.679556 -75.752991 $ 55 Delaware State 39.185668 -75.544091 $ 72 Maryland 38.985944 -76.938586 $ 56 Md.-Eastern Shore 38.207344 -75.686038 $ 64 Navy 38.982056 -76.483016 $ ____________________________________________________________________________________________________ SECTIONAL#11 total miles=782 average distance between teams=78 pairs=10 teams=5 58 Binghamton-NY 42.089797 -75.968254 $ 71 Bucknell 40.955363 -76.884133 $ 54 Colgate 42.817292 -75.535735 $ 63 Cornell 42.447017 -76.482996 $ 59 Syracuse 43.037844 -76.134646 $ ____________________________________________________________________________________________________ SECTIONAL#12 total miles=702 average distance between teams=47 pairs=15 teams=6 62 Hampton 37.019869 -76.338833 $ 60 Norfolk State 36.849592 -76.262717 $ 61 Old Dominion 36.890148 -76.304386 $ 81 Richmond 37.576257 -77.537487 $ 80 Va. Commonwealth 37.547646 -77.456095 $ 69 William & Mary 37.271536 -76.711624 $ ____________________________________________________________________________________________________ SECTIONAL#13 total miles=284 average distance between teams=19 pairs=15 teams=6 68 Coppin State 39.310384 -76.658303 $ 67 Loyola-Maryland 39.346496 -76.619135 $ 65 Morgan State 39.345940 -76.583022 $ 78 Mount St. Mary's 39.681764 -77.353042 $ 66 Towson 39.392329 -76.605801 $ 70 UMBC(Md-Balt) 39.255384 -76.711637 $ ____________________________________________________________________________________________________ SECTIONAL#14 total miles=579 average distance between teams=39 pairs=15 teams=6 76 American U. 38.937055 -77.086922 $ 77 George Mason 38.834002 -77.308596 $ 74 George Washington 38.898723 -77.045810 $ 75 Georgetown 38.907334 -77.072200 $ 73 Howard 38.923722 -77.021366 $ 92 James Madison 38.438180 -78.873360 $ ____________________________________________________________________________________________________ SECTIONAL#15 total miles=1067 average distance between teams=71 pairs=15 teams=6 89 Campbell 35.409883 -78.740295 $ 94 Duke 35.997527 -78.942317 $ 79 East Carolina 35.600439 -77.364409 $ 93 NC Central 35.974276 -78.898605 $ 88 NC State 35.786589 -78.670735 $ 83 NC Wilmington 34.226837 -77.876930 $ ____________________________________________________________________________________________________ SECTIONAL#16 total miles=817 average distance between teams=82 pairs=10 teams=5 90 Buffalo 42.953113 -78.820868 $ 91 Canisius 42.925336 -78.852535 $ 96 Niagara 43.138666 -79.038933 $ 82 Penn State 40.803950 -77.857224 $ 85 St. Bonaventure 42.079787 -78.482522 $ ____________________________________________________________________________________________________ SECTIONAL#17 total miles=1084 average distance between teams=72 pairs=15 teams=6 98 Liberty 37.350977 -79.180579 $ 84 Longwood 37.300430 -78.395551 $ 116 Radford 37.139015 -80.549502 $ 99 VMI 37.789576 -79.439482 $ 86 Virginia 38.035417 -78.503346 $ 115 Virginia Tech 37.228740 -80.423662 $ ____________________________________________________________________________________________________ SECTIONAL#18 total miles=476 average distance between teams=48 pairs=10 teams=5 107 Duquesne 40.436180 -79.992831 $ 105 Pittsburgh 40.442847 -79.959219 $ 109 Robert Morris 40.438958 -79.993664 $ 87 St. Francis-Pa. 40.504237 -78.637518 $ 104 West Virginia 39.634248 -79.954508 $ ____________________________________________________________________________________________________ SECTIONAL#19 total miles=448 average distance between teams=30 pairs=15 teams=6 100 Elon 36.107080 -79.505856 $ 108 High Point 35.972081 -79.993650 $ 101 N.C. A&T 36.073746 -79.776419 $ 102 NC Greensboro 36.070969 -79.811143 $ 97 North Carolina 35.899514 -79.043930 $ 112 Wake Forest 36.133471 -80.277273 $ ____________________________________________________________________________________________________ SECTIONAL#20 total miles=1203 average distance between teams=80 pairs=15 teams=6 110 Charleston Southern 32.977127 -80.069864 $ 106 Citadel 32.796010 -79.959256 $ 95 Coastal Carolina 33.793782 -79.011979 $ 103 College of Charleston 32.784065 -79.937033 $ 134 Georgia Southern 32.425456 -81.783445 $ 120 South Carolina State 33.498444 -80.848123 $ ____________________________________________________________________________________________________ SECTIONAL#21 total miles=584 average distance between teams=58 pairs=10 teams=5 118 Charlotte 35.305142 -80.732014 $ 119 Davidson 35.500136 -80.845073 $ 130 Gardner-Webb 35.247625 -81.670374 $ 121 South Carolina 33.999044 -81.026481 $ 122 Winthrop 34.940700 -81.028411 $ ____________________________________________________________________________________________________ SECTIONAL#22 total miles=1118 average distance between teams=112 pairs=10 teams=5 111 Florida Atlantic 26.371188 -80.102543 $ 133 Florida Gulf Coast 26.471045 -81.764672 $ 114 Florida International 25.754267 -80.381998 $ 113 Miami-Florida 25.719546 -80.278662 $ 142 South Florida 28.062795 -82.412315 $ ____________________________________________________________________________________________________ SECTIONAL#23 total miles=1077 average distance between teams=72 pairs=15 teams=6 123 Bethune-Cookman 29.210259 -81.035056 $ 124 Central Florida(UCF) 28.600277 -81.202010 $ 139 Florida 29.648579 -82.349271 $ 129 Jacksonville 30.352462 -81.605371 $ 127 North Florida(UNF) 30.269963 -81.507033 $ 125 Stetson 29.035540 -81.303396 $ ____________________________________________________________________________________________________ SECTIONAL#24 total miles=712 average distance between teams=71 pairs=10 teams=5 128 Akron 41.076167 -81.511505 $ 131 Cleveland State 41.503107 -81.672908 $ 126 Kent State 41.147834 -81.338441 $ 146 Ohio State 39.996175 -83.018795 $ 117 Youngstown State 41.104225 -80.647019 $ ____________________________________________________________________________________________________ SECTIONAL#25 total miles=362 average distance between teams=36 pairs=10 teams=5 145 Clemson 34.677049 -82.838754 $ 141 Furman 34.841784 -82.401789 $ 135 Presbyterian College 34.465072 -81.868978 $ 137 USC Upstate 34.995684 -81.968813 $ 136 Wofford 34.959011 -81.935382 $ ____________________________________________________________________________________________________ SECTIONAL#26 total miles=739 average distance between teams=74 pairs=10 teams=5 132 Appalachian State 36.214573 -81.680385 $ 140 East Tennessee State 36.303440 -82.369029 $ 144 NC Asheville 35.618167 -82.565683 $ 157 Tennessee 35.954249 -83.930740 $ 148 Western Carolina 35.310933 -83.181811 $ ____________________________________________________________________________________________________ SECTIONAL#27 total miles=691 average distance between teams=46 pairs=15 teams=6 154 Bowling Green 41.375886 -83.639656 $ 147 Detroit 42.332260 -83.037976 $ 153 Eastern Michigan 42.246983 -83.622716 $ 156 Michigan 42.275872 -83.736052 $ 149 Oakland-Mich. 42.675866 -83.217713 $ 152 Toledo 41.661994 -83.614380 $ ____________________________________________________________________________________________________ SECTIONAL#28 total miles=915 average distance between teams=91 pairs=10 teams=5 162 Eastern Kentucky 37.738135 -84.301599 $ 168 Kentucky 38.030355 -84.499383 $ 143 Marshall 38.423139 -82.430431 $ 151 Morehead State 38.186748 -83.433240 $ 138 Ohio U. 39.323129 -82.095422 $ ____________________________________________________________________________________________________ SECTIONAL#29 total miles=1166 average distance between teams=78 pairs=15 teams=6 174 Chattanooga 35.046185 -85.300235 $ 150 Georgia 33.951226 -83.373769 $ 163 Georgia State 33.752884 -84.386038 $ 164 Georgia Tech 33.772884 -84.393816 $ 170 Kennesaw State 34.037600 -84.585211 $ 155 Mercer 32.831806 -83.649903 $ ____________________________________________________________________________________________________ SECTIONAL#30 total miles=489 average distance between teams=33 pairs=15 teams=6 169 Cincinnati 39.131448 -84.516332 $ 159 Dayton 39.739781 -84.178273 $ 171 Miami-Ohio 39.509220 -84.734120 $ 165 Northern Kentucky 39.031970 -84.459136 $ 158 Wright State 39.783670 -84.063547 $ 166 Xavier-Ohio 39.149782 -84.477998 $ ____________________________________________________________________________________________________ SECTIONAL#31 total miles=1116 average distance between teams=112 pairs=10 teams=5 186 Alabama State 32.364027 -86.295524 $ 176 Auburn 32.602079 -85.484949 $ 160 Florida A&M 30.426867 -84.285177 $ 161 Florida State 30.440756 -84.291844 $ 182 Troy 31.800713 -85.957173 $ ____________________________________________________________________________________________________ SECTIONAL#32 total miles=987 average distance between teams=99 pairs=10 teams=5 172 Central Michigan 43.591419 -84.775014 $ 173 IPFW 41.116715 -85.097192 $ 167 Michigan State 42.730868 -84.478587 $ 185 Notre Dame 41.703104 -86.239173 $ 178 Western Michigan 42.283651 -85.611951 $ ____________________________________________________________________________________________________ SECTIONAL#33 total miles=1175 average distance between teams=78 pairs=15 teams=6 175 Ball State 40.199488 -85.412471 $ 179 Bellarmine 38.221627 -85.705030 $ 183 Butler 39.838930 -86.172488 $ 184 IUPUI 39.776432 -86.185265 $ 189 Indiana 39.166158 -86.526386 $ 180 Louisville 38.215071 -85.759129 $ ____________________________________________________________________________________________________ SECTIONAL#34 total miles=487 average distance between teams=32 pairs=15 teams=6 192 Belmont 36.135613 -86.794721 $ 193 Lipscomb 36.105614 -86.799444 $ 187 Middle Tennessee 35.852288 -86.369992 $ 196 Tennessee State 36.167279 -86.830555 $ 177 Tennessee Tech 36.174505 -85.503865 $ 195 Vanderbilt 36.148113 -86.803055 $ ____________________________________________________________________________________________________ SECTIONAL#35 total miles=1231 average distance between teams=82 pairs=15 teams=6 202 Alabama 33.215118 -87.546673 $ 190 Alabama A&M 34.785646 -86.569159 $ 181 Jacksonville State 33.822323 -85.766632 $ 208 North Alabama 34.808470 -87.683769 $ 191 Samford 33.465107 -86.793323 $ 194 UAB 33.504828 -86.799990 $ ____________________________________________________________________________________________________ SECTIONAL#36 total miles=334 average distance between teams=22 pairs=15 teams=6 203 Chicago State 41.718090 -87.608659 $ 205 DePaul 41.922810 -87.653110 $ 204 Illinois-Chicago 41.871977 -87.649220 $ 206 Loyola-Chicago 42.000587 -87.658112 $ 207 Northwestern 42.055586 -87.674503 $ 198 Valparaiso 41.462539 -87.043641 $ ____________________________________________________________________________________________________ SECTIONAL#37 total miles=1491 average distance between teams=99 pairs=15 teams=6 199 Austin Peay 36.533382 -87.353897 $ 201 Evansville 37.971709 -87.531681 $ 215 Murray State 36.611445 -88.322261 $ 223 SE Missouri State 37.312551 -89.530926 $ 218 Tennessee-Martin 36.341452 -88.864227 $ 188 Western Kentucky 36.987542 -86.451658 $ ____________________________________________________________________________________________________ SECTIONAL#38 total miles=1256 average distance between teams=84 pairs=15 teams=6 225 Bradley 40.698093 -89.617043 $ 212 Eastern Illinois 39.480590 -88.175596 $ 214 Illinois 40.108643 -88.228382 $ 219 Illinois State 40.512536 -88.997576 $ 200 Indiana State 39.468648 -87.408631 $ 197 Purdue 40.428091 -86.922510 $ ____________________________________________________________________________________________________ SECTIONAL#39 total miles=932 average distance between teams=93 pairs=10 teams=5 211 Marquette 43.037514 -87.929807 $ 216 Northern Illinois 41.937529 -88.775921 $ 210 Wis.-Green Bay 44.529993 -87.920934 $ 209 Wis.-Milwaukee 43.075568 -87.878973 $ 222 Wisconsin 43.073885 -89.410953 $ ____________________________________________________________________________________________________ SECTIONAL#40 total miles=1354 average distance between teams=135 pairs=10 teams=5 230 Jackson State 32.295980 -90.207866 $ 232 MVSU(Mississippi Valley St.) 33.515120 -90.338696 $ 217 Mississippi State 33.454844 -88.788664 $ 213 South Alabama 30.694912 -88.179725 $ 221 Southern Mississippi 31.326563 -89.332285 $ ____________________________________________________________________________________________________ SECTIONAL#41 total miles=726 average distance between teams=48 pairs=15 teams=6 238 LSU 30.414636 -91.176218 $ 228 New Orleans 30.027980 -90.067016 $ 236 Nicholls State 29.794375 -90.802037 $ 233 SE Louisiana 30.515191 -90.471200 $ 239 Southern University 30.523522 -91.190386 $ 229 Tulane 29.939927 -90.119518 $ ____________________________________________________________________________________________________ SECTIONAL#42 total miles=1378 average distance between teams=138 pairs=10 teams=5 244 Missouri 38.945872 -92.327684 $ 253 Missouri State 37.198382 -93.278520 $ 227 SIU-Edwardsville 38.796333 -89.999826 $ 231 Saint Louis 38.635329 -90.233723 $ 220 Southern Illinois 37.713106 -89.218695 $ ____________________________________________________________________________________________________ SECTIONAL#43 total miles=1630 average distance between teams=109 pairs=15 teams=6 245 Ark.-Little Rock 34.721759 -92.341264 $ 242 Ark.-Pine Bluff 34.242320 -92.019585 $ 234 Arkansas State 35.843130 -90.677056 $ 246 Central Arkansas 35.079252 -92.457102 $ 226 Memphis 35.118701 -89.937311 $ 224 Mississippi 34.366773 -89.535360 $ ____________________________________________________________________________________________________ SECTIONAL#44 total miles=1396 average distance between teams=93 pairs=15 teams=6 237 Alcorn State 31.877105 -91.141220 $ 249 Grambling 32.525428 -92.715152 $ 248 Louisiana Tech 32.527372 -92.646260 $ 241 Louisiana-Lafayette 30.215479 -92.019009 $ 243 Louisiana-Monroe 32.526532 -92.074578 $ 250 Northwestern State 31.753220 -93.097664 $ ____________________________________________________________________________________________________ SECTIONAL#45 total miles=1109 average distance between teams=111 pairs=10 teams=5 255 Drake 41.601378 -93.651886 $ 240 Iowa 41.661683 -91.536280 $ 254 Iowa State 42.026097 -93.648552 $ 247 Northern Iowa 42.515818 -92.457410 $ 235 Western Illinois 40.464208 -90.683742 $ ____________________________________________________________________________________________________ SECTIONAL#46 total miles=980 average distance between teams=65 pairs=15 teams=6 261 Houston 29.720507 -95.343549 $ 264 Houston Baptist 29.694786 -95.517220 $ 256 Lamar 29.879382 -93.926837 $ 251 McNeese State 30.180485 -93.217376 $ 263 Rice 29.719118 -95.397439 $ 262 Texas Southern 29.722729 -95.360772 $ ____________________________________________________________________________________________________ SECTIONAL#47 total miles=1708 average distance between teams=114 pairs=15 teams=6 267 Creighton 41.265276 -95.947514 $ 260 Kansas 38.958058 -95.247750 $ 272 Kansas State 39.200400 -96.588400 $ 273 Nebraska 40.817779 -96.701683 $ 270 Nebraska-Omaha 41.257087 -96.008717 $ 258 UMKC 39.035005 -94.577178 $ ____________________________________________________________________________________________________ SECTIONAL#48 total miles=2156 average distance between teams=216 pairs=10 teams=5 252 Minnesota 44.974410 -93.233002 $ 279 North Dakota 47.927668 -97.071444 $ 276 North Dakota State 46.894687 -96.803415 $ 277 South Dakota 42.783118 -96.924328 $ 274 South Dakota State 44.319431 -96.783275 $ ____________________________________________________________________________________________________ SECTIONAL#49 total miles=1555 average distance between teams=104 pairs=15 teams=6 280 Baylor 31.544889 -97.119446 $ 269 Prairie View A&M 30.092163 -95.989678 $ 265 Sam Houston State 30.714360 -95.549388 $ 259 Stephen F. Austin 31.621568 -94.649376 $ 287 Texas 30.286041 -97.738894 $ 271 Texas A&M 30.617700 -96.338296 $ ____________________________________________________________________________________________________ SECTIONAL#50 total miles=1723 average distance between teams=115 pairs=15 teams=6 257 Arkansas 36.068691 -94.172149 $ 286 Oklahoma 35.203956 -97.444478 $ 278 Oklahoma State 36.121995 -97.070313 $ 268 Oral Roberts 36.049262 -95.951105 $ 266 Tulsa 36.152316 -95.946106 $ 283 Wichita State 37.719180 -97.293378 $ ____________________________________________________________________________________________________ SECTIONAL#51 total miles=1202 average distance between teams=80 pairs=15 teams=6 293 Abilene Christian 32.470381 -99.709113 $ 282 North Texas 33.211508 -97.150013 $ 275 SMU 32.845127 -96.784167 $ 285 TCU 32.709298 -97.361684 $ 290 Tarleton State 32.215569 -98.219980 $ 281 Texas-Arlington 32.729298 -97.126677 $ ____________________________________________________________________________________________________ SECTIONAL#52 total miles=1348 average distance between teams=135 pairs=10 teams=5 291 Incarnate Word 29.468072 -98.469261 $ 284 Texas A&M-CorpusChristi 27.714198 -97.324713 $ 288 Texas State 29.889941 -97.939450 $ 289 Texas-Pan American 26.309793 -98.174177 $ 292 Texas-San Antonio 29.577172 -98.622799 $ ____________________________________________________________________________________________________ SECTIONAL#53 total miles=1085 average distance between teams=72 pairs=15 teams=6 296 Air Force 38.990270 -104.858313 $ 299 Colorado 40.005541 -105.264434 $ 298 Colorado State 40.574982 -105.083867 $ 297 Denver 39.676654 -104.962203 $ 295 Northern Colorado 40.409981 -104.693021 $ 300 Wyoming 41.311923 -105.576378 $ ____________________________________________________________________________________________________ SECTIONAL#54 total miles=2707 average distance between teams=271 pairs=10 teams=5 304 Arizona 32.231187 -110.952591 $ 302 New Mexico 35.083936 -106.619191 $ 303 New Mexico State 32.283428 -106.753336 $ 294 Texas Tech 33.585918 -101.871834 $ 301 UTEP 31.777608 -106.506099 $ ____________________________________________________________________________________________________ SECTIONAL#55 total miles=1485 average distance between teams=149 pairs=10 teams=5 306 BYU 40.245788 -111.651033 $ 316 Dixie State 37.101419 -113.567044 $ 315 Southern Utah 37.675531 -113.072925 $ 310 Utah 40.764946 -111.848546 $ 308 Utah Valley State 40.289398 -111.706315 $ ____________________________________________________________________________________________________ SECTIONAL#56 total miles=2047 average distance between teams=205 pairs=10 teams=5 319 Boise State 43.602945 -116.198450 $ 314 Idaho State 42.866859 -112.433312 $ 305 Montana State 45.669652 -111.053003 $ 309 Utah State 41.741042 -111.812721 $ 312 Weber State 41.211055 -111.944385 $ ____________________________________________________________________________________________________ SECTIONAL#57 total miles=2110 average distance between teams=211 pairs=10 teams=5 311 Arizona State 33.417268 -111.935421 $ 313 Grand Canyon 33.510017 -112.130826 $ 307 Northern Arizona 35.190012 -111.658217 $ 325 UC Riverside 33.973349 -117.330877 $ 318 UNLV 36.107750 -115.141665 $ ____________________________________________________________________________________________________ SECTIONAL#58 total miles=910 average distance between teams=91 pairs=10 teams=5 328 Eastern Washington 47.489889 -117.582985 $ 326 Gonzaga 47.665725 -117.402435 $ 320 Idaho 46.725721 -117.011276 $ 317 Montana 46.860202 -113.983720 $ 322 Washington State 46.730997 -117.158226 $ ____________________________________________________________________________________________________ SECTIONAL#59 total miles=503 average distance between teams=50 pairs=10 teams=5 327 California Baptist 33.926835 -117.422312 $ 323 San Diego 32.771994 -117.191701 $ 321 San Diego State 32.776717 -117.070864 $ 329 UC Irvine 33.646132 -117.842833 $ 324 UC San Diego 32.885116 -117.239165 $ ____________________________________________________________________________________________________ SECTIONAL#60 total miles=344 average distance between teams=23 pairs=15 teams=6 330 CS Fullerton 33.880292 -117.885615 $ 331 Long Beach State 33.776406 -118.114232 $ 333 Loyola Marymount 33.970846 -118.416744 $ 336 Pepperdine 34.040563 -118.709253 $ 332 Southern California 34.020846 -118.285630 $ 334 UCLA 34.071398 -118.438413 $ ____________________________________________________________________________________________________ SECTIONAL#61 total miles=1131 average distance between teams=113 pairs=10 teams=5 337 CS Bakersfield 35.372504 -119.012900 $ 335 CS Northridge 34.238615 -118.531197 $ 341 Cal Poly-SLO 35.300808 -120.660727 $ 338 Fresno State 36.812450 -119.746533 $ 340 UC Santa Barbara 34.416107 -119.849027 $ ____________________________________________________________________________________________________ SECTIONAL#62 total miles=1159 average distance between teams=77 pairs=15 teams=6 349 California 37.869648 -122.258858 $ 339 Nevada 39.541577 -119.814914 $ 342 Pacific 37.979645 -121.311336 $ 343 Sacramento State 38.562684 -121.424120 $ 347 Saint Mary's-Cal. 37.841037 -122.108020 $ 344 UC Davis 38.540184 -121.749128 $ ____________________________________________________________________________________________________ SECTIONAL#63 total miles=9767 average distance between teams=977 pairs=10 teams=5 357 Hawaii 21.300278 -157.823056 $ 352 San Francisco 37.775485 -122.450805 $ 345 San Jose State 37.334386 -121.881066 $ 346 Santa Clara 37.349108 -121.939957 $ 348 Stanford 37.427161 -122.170242 $ ____________________________________________________________________________________________________ SECTIONAL#64 total miles=1921 average distance between teams=128 pairs=15 teams=6 355 Oregon 44.035125 -123.084531 $ 356 Oregon State 44.567344 -123.278155 $ 354 Portland 45.572062 -122.724265 $ 353 Portland State 45.512063 -122.683707 $ 351 Seattle 47.607629 -122.313223 $ 350 Washington 47.656209 -122.306515 $ ____________________________________________________________________________________________________ ____________________________________________________________________________________________________ Explanation of Data It's really hard to get the exact solution other than literally checking every possible combination but with 402 Indiana high school(345 in NCAA division I) teams, you can see that the factorial issue soon makes that impossible on even the best PC's and in fact for even the fastest super-computers. In fact, for the Indiana High Schools, based on there being 46 sectionals with 6 teams and 18 sectionals with 7 teams, I think it would be: 402! ____________________________________ (6!)^46 * (7!)^18 And the natural logarithm of the answer is 1556.3926512477 and thus the logbase10 of the answer is 675.9327401116 which means the number of possible combinations is 10^675.9327401116 which is an amazingly large number! It would be actually be an exact integer, but I don't have access to a computer that can handle such large integers. I think only the latest "super computers" can. For college basketball with 357 teams with 27 sectionals with 5 teams and 37 sectionals with 6 teams, it would be: 357! ____________________________________ = 10^596.0757525196 which is also a number beyond the capacity to (5!)^27 * (6!)^37 simply "try all the possibilities". NOTE: I originally had underestimated these quantities by having (incorrectly) an additional factor of 64! in the denominators. An observant reader named Loren Maxwell alerted me to this and so it's been corrected. Remember, there are 31.5576 million seconds in an average year or 3.16 * 10^7 seconds. Thus for even a super-computer to check every possibility in one-year, it would have to evaluate more than 10^668 possibilities per second for the high schools and more than 10^588 per second for the colleges. So the simulated annealing technique is used to avoid the impossible task of literally checking every possibility. It was first developed in the early 1950s at Los Alamos by guys like Edward Teller when they (Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M.; Teller, A. H.; and Teller, E. "Equation of State Calculations by Fast Computing Machines." J. Chem. Phys. 21, 1087-1092, 1953. ) were working on the hydrogen bomb. I was in my early oughts then and so was only consulting with them on an informal basis :-) (just kidding!) at that time.
[ Monte Carlo Landmark Papers ]

[ Equation of State Calculations by Fast Computing Machines ]

> Equation of State Calculations by Fast Computing Machines
> N. Metropolis, A.W.Rosenbluth, M.N.Rosenbluth, A.H.Teller and E. Teller 1953
> The Journal of Chemical Physics, 21, 1087 (1953)
> THE paper. Probably THE most important algorithm of the 20th century, often called the M(RT)2 algorithm from the names of the authors.
  (the paper begins in the middle of page 1087)


The exact same technique could be used to redistrict
for congressional and state districts if you were to treat each
voter as a "team".  And each district would end up with very close to the
same number of voters and those voters would all be close to each other
geographically.  No more ludicrously shaped districts created totally for the
purpose of giving an advantage to the party drawing the lines.
Of course you'd need to use the supercomputers at the major universities
because even using simulated annealing would take a very long time with
several million "teams(voters)" in each state :-D

But the neat thing about this is that each party could have a mathematician
who liked them run the program and they'd either both get the same answer,
or the one with the lower total distance would have the better answer.
The fact that this would literally "take politics out of the equation", is probably
the reason that it wouldn't be adopted;  each party would worry that an honest
redistricting could take away "their" safe seats.
Enjoy!
Jeff Sagarin
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