| Game |
| Result | Moves |
Year |
Event/Locale | Opening |
| 1. J Cuartas Medina vs J M Bellon Lopez |
| ½-½ | 61 |
2001 |
IX Guillermo Garcia Mem | B40 Sicilian |
| 2. J Cuartas Medina vs C Michel Yunis |
| ½-½ | 72 |
2001 |
IX Guillermo Garcia Mem | B05 Alekhine's Defense, Modern |
| 3. R Perez vs J Cuartas Medina |
| ½-½ | 40 |
2001 |
IX Guillermo Garcia Mem | B10 Caro-Kann |
| 4. J Cuartas Medina vs L Bruzon |
| ½-½ | 50 |
2001 |
I American Continental | B47 Sicilian, Taimanov (Bastrikov) Variation |
| 5. J Cuartas Medina vs M Heidenfeld |
| ½-½ | 45 |
2002 |
Bled Olympiad | C03 French, Tarrasch |
| 6. J Cuartas Medina vs Gulko |
| ½-½ | 49 |
2002 |
Bled Olympiad | B30 Sicilian |
| 7. E Cordova vs J Cuartas Medina |
| ½-½ | 57 |
2004 |
36th Olympiad | A43 Old Benoni |
| 8. J Gonzales vs J Cuartas Medina |
| ½-½ | 41 |
2004 |
36th Olympiad | A09 Reti Opening |
| 9. C Davila vs J Cuartas Medina |
| ½-½ | 62 |
2004 |
36th Olympiad | B13 Caro-Kann, Exchange |
| 10. J Cuartas Medina vs D Erhembayar |
| ½-½ | 86 |
2004 |
36th Olympiad | B22 Sicilian, Alapin |
| 11. S Sulskis vs J Cuartas Medina |
| ½-½ | 90 |
2004 |
36th Olympiad | B10 Caro-Kann |
| 12. J Cuartas Medina vs G Soppe |
| ½-½ | 36 |
2004 |
36th Olympiad | B04 Alekhine's Defense, Modern |
| 13. J Cuartas Medina vs O Korneev |
| ½-½ | 24 |
2005 |
Magistral Huila 100 aņos - Neiva | C80 Ruy Lopez, Open |
| 14. V Dobrov vs J Cuartas Medina |
| ½-½ | 26 |
2005 |
Magistral Huila 100 aņos - Neiva | D90 Grunfeld |
| 15. J Cuartas Medina vs Granda-Zuniga |
| ½-½ | 47 |
2005 |
Magistral Huila 100 aņos - Neiva | B51 Sicilian, Canal-Sokolsky (Rossolimo) Attack |
| 16. J Cuartas Medina vs M Paragua |
| ½-½ | 52 |
2006 |
37th Chess Olympiad | B51 Sicilian, Canal-Sokolsky (Rossolimo) Attack |
| 17. M Marin vs J Cuartas Medina |
| ½-½ | 37 |
2006 |
VIII Sants Open | A22 English |
| 18. J Cuartas Medina vs J M Lopez Martinez |
 | ½-½ | 86 |
2006 |
XXIX Open Barbera del Valles | C65 Ruy Lopez, Berlin Defense |
| 19. Jobava vs J Cuartas Medina |
| ½-½ | 66 |
2006 |
37th Chess Olympiad | D90 Grunfeld |
| 20. V Moskalenko vs J Cuartas Medina |
| ½-½ | 38 |
2006 |
VIII Sants Open | D13 Queen's Gambit Declined Slav, Exchange Variation |
| 21. J Cuartas Medina vs R Kozlov |
| ½-½ | 53 |
2006 |
37th Chess Olympiad | B31 Sicilian, Rossolimo Variation |
| 22. J Cuartas Medina vs R Felgaer |
| ½-½ | 31 |
2006 |
VIII Sants Open | B22 Sicilian, Alapin |
| 23. J Cuartas Medina vs N Mitkov |
| ½-½ | 50 |
2006 |
37th Chess Olympiad | C65 Ruy Lopez, Berlin Defense |
| 24. J Cuartas Medina vs V Bach |
 | ½-½ | 39 |
2006 |
XXIX Open Barbera del Valles | B42 Sicilian, Kan |
| 25. J Cuartas Medina vs M Mahjoob |
| ½-½ | 9 |
2006 |
37th Chess Olympiad | B42 Sicilian, Kan |