4 letters:
1. University of San Francisco Dons
2. Temple Owls
3. Colorado State University Rams
5 letters:
4. North Dakota State Bison
5. Oregon Ducks
6. James Madison University Dukes
7. Saint Mary's College Gaels
8. Georgetown Hoyas
9. University of New Mexico Lobos
6 letters:
10. Texas A&M Aggies
11. San Diego State Aztecs
12. U.C.L.A Bruins
13. Boston College Eagles
14. Florida Gators
15. Virginia Tech Hokies
16. Sienna College Saints
17. Clemson Tigers
7 letters:
18. Wisconsin Badgers
19. Ohio University Bobcats
20. Boise State Broncos
21. Wyoming Cowboys
22. Air Force Falcons
23. University of Connecticut Huskies
24. Seton Hall Pirates
25. Oklahoma Sooners
26. University of Richmond Spiders
27. University of Southern California Trojans
8 letters:
28. Cincinnati Bearcats
29. Georgia Bulldogs
30. Stanford Cardinal
31. George Mason Patriots
32. Denver Pioneers
33. Michigan State Spartans
34. Kentucky Wildcats
9 letters:
35. University of Virginia Cavaliers
36. University of South Carolina Gamecocks
37. University of Texas Longhorns
38. University of Maryland Terrapins
10 letters:
39. Vanderbilt Commodores
40. Duke University Blue Devils
Begin by placing the three four letter words and the two ten letter words in the puzzle.
In the top line, COMMODORES must fit because BLUEDEVILS would give you a four letter word beginning with V (and there is none). So, BLUEDEVILS must go down on the bottom line. Then RAMS can be placed in its correct position (OWLS must crisscross with COMMODORES since it is the only 4-letter word beginning with O). RAMS can be placed in its correct position at the top of the grid because the 7th letter of the 8-letter word on the top line must be an R. So, you can fill in DONS and PIONEERS. Then BISON can be positioned since it is the only nickname to end in N.
SAINTS can be put in its position because it is the only six-letter word beginning with S. Then PIRATES follows because it is the only seven letter word that begins with P.
The next word is a little harder to determine. The word that crisscrosses PIRATES is 8 letters long and the fourth letter must be an R. But there are three words that fit: PATRIOTS, SPARTANS, and BEARCATS. Note that the second letter of this word must be the same as the third letter of another eight letter word that crisscrosses it. So, that eliminates BEARCATS, because none of the other eight letter words have an E in the third position. Similarly, SPARTANS can be eliminated for the same reason (none of the other eight letter words has a P in the third position). So, PATRIOTS can be placed in its position.
TIGERS is the next word to be placed because it is the only 6-letter word beginning with T. Then TERRAPINS is the only 9-letter word whose second letter is an E. SPARTANS is the only 8-letter word left that has P for its second letter. That leaves BEARCATS as the only remaining 8-letter word with A as its third letter.
TROJANS can be positioned because only two 7-letter words have an R for the second letter (the other is BRONCOS). But the fifth letter of TROJANS is an A and the fifth letter of BRONCOS is an O. There is no 6-letter word beginning with O, so TROJANS can be placed in its position. AZTECS is the only 6-letter word that begins with A and also works with SPARTANS.
CARDINAL is the only 8-letter beginning with a C. Then CAVLIERS is the only 9-letter word whose 5th letter is an L. EAGLES is the only 6-letter word that begins with an E.
BULLDOGS is the only 8-letter word whose 7th letter is a G. WILDCATS is the only remaining 8-letter word, so it can be placed. LOBOS is the only 5-letter word beginning with an L.
GAMECOCKS and LONGHORNS must intersect each other since they are the only 9-letter words left, so they can be put into position. HOKIES is the only 6-letter word with the second letter O.
FALCONS and BADGERS are the only 7-letter words with the second letter A. Then cross check with the 7-letter words with the third letter O: BRONCOS and SOONERS. Since the 6th letter must be either an O or an E, the two crosswords must be FALCONS and BRONCOS.
The two 7-letter words left are BADGERS and BOBCATS. Of the remaining 6-letter words, only BRUINS fits because it has an R in the second letter. SOONERS is the only 7-letter word left whose 4th letter is an N. SPIDERS is the only 7-letter word beginning with S, and HUSKIES is the only 7-letter word whose third letter is S.
The two 7-letter words left are BOBCATS and COWBOYS. The 5th letter cannot be an O because the 6-letter crosswords are AGGIES and GATORS. So, we can place BOBCATS and AGGIES. Then GATORS follows, and then COWBOYS after that, and then HOYAS.
The last three words can only be placed in one way with DUKES and DUCKS intersecting. Then GAELS must fit in the last spaces..
So, here is the order in which the nicknames could be positioned (several of them can be interchanged):
1. COMMODORES
2. BLUE DEVILS
3. OWLS
4. RAMS
5. DONS
6. PIONEERS
7. BISON
8. SAINTS
9. PIRATES
10. PATRIOTS
11. TIGERS
12. TERRAPINS
13. SPARTANS
14. BEARCATS
15. TROJANS
16. AZTECS
17. CARDINAL
18. CAVALIERS
19. EAGLES
20. BULLDOGS
21. WILDCATS
22. LOBOS
23. GAMECOCKS
24. LONGHORNS
25. HOKIES
26. FALCONS
27. BRONCOS
28. BRUINS
29. BADGERS
30. SOONERS
31. SPIDERS
32. HUSKIES
33. BOBCATS
34. AGGIES
35. GATORS
36. COWBOYS
37. HOYAS
38. DUKES
39. DUCKS
40. GAELS