Maximum number of diagonal transversals in a diagonal Latin square of order n, https://oeis.org/A287648 n=1, a(1)=1 Article: E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, S. Yu. Valyaev, Enumerating the Transversals for Diagonal Latin Squares of Small Order. CEUR Workshop Proceedings. Proceedings of the Third International Conference BOINC-based High Performance Computing: Fundamental Research and Development (BOINC:FAST 2017). Vol. 1973. Technical University of Aachen, Germany, 2017. pp. 6-14. urn:nbn:de:0074-1973-0. http://ceur-ws.org/Vol-1973/paper01.pdf Way of finding: brute force 0 n=2, a(2)=0 - n=3, a(3)=0 - n=4, a(4)=4 Article: E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, S. Yu. Valyaev, Enumerating the Transversals for Diagonal Latin Squares of Small Order. CEUR Workshop Proceedings. Proceedings of the Third International Conference BOINC-based High Performance Computing: Fundamental Research and Development (BOINC:FAST 2017). Vol. 1973. Technical University of Aachen, Germany, 2017. pp. 6-14. urn:nbn:de:0074-1973-0. http://ceur-ws.org/Vol-1973/paper01.pdf Way of finding: brute force 0 1 2 3 3 2 1 0 1 0 3 2 2 3 0 1 n=5, a(5)=5 Article: E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, S. Yu. Valyaev, Enumerating the Transversals for Diagonal Latin Squares of Small Order. CEUR Workshop Proceedings. Proceedings of the Third International Conference BOINC-based High Performance Computing: Fundamental Research and Development (BOINC:FAST 2017). Vol. 1973. Technical University of Aachen, Germany, 2017. pp. 6-14. urn:nbn:de:0074-1973-0. http://ceur-ws.org/Vol-1973/paper01.pdf Way of finding: brute force 0 1 2 3 4 4 2 3 0 1 3 4 1 2 0 1 3 0 4 2 2 0 4 1 3 n=6, a(6)=6 Article: E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, S. Yu. Valyaev, Enumerating the Transversals for Diagonal Latin Squares of Small Order. CEUR Workshop Proceedings. Proceedings of the Third International Conference BOINC-based High Performance Computing: Fundamental Research and Development (BOINC:FAST 2017). Vol. 1973. Technical University of Aachen, Germany, 2017. pp. 6-14. urn:nbn:de:0074-1973-0. http://ceur-ws.org/Vol-1973/paper01.pdf Way of finding: brute force 0 1 2 3 4 5 4 2 5 1 3 0 3 5 1 2 0 4 5 3 0 4 1 2 2 4 3 0 5 1 1 0 4 5 2 3 n=7, a(7)=27 Article: E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, S. Yu. Valyaev, Enumerating the Transversals for Diagonal Latin Squares of Small Order. CEUR Workshop Proceedings. Proceedings of the Third International Conference BOINC-based High Performance Computing: Fundamental Research and Development (BOINC:FAST 2017). Vol. 1973. Technical University of Aachen, Germany, 2017. pp. 6-14. urn:nbn:de:0074-1973-0. http://ceur-ws.org/Vol-1973/paper01.pdf Way of finding: brute force 0 1 2 3 4 5 6 4 2 6 0 5 1 3 3 5 1 6 0 4 2 5 6 3 4 1 2 0 6 4 5 2 3 0 1 1 3 0 5 2 6 4 2 0 4 1 6 3 5 n=8, a(8)=120 Article: E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, S. Yu. Valyaev, Enumerating the Transversals for Diagonal Latin Squares of Small Order. CEUR Workshop Proceedings. Proceedings of the Third International Conference BOINC-based High Performance Computing: Fundamental Research and Development (BOINC:FAST 2017). Vol. 1973. Technical University of Aachen, Germany, 2017. pp. 6-14. urn:nbn:de:0074-1973-0. http://ceur-ws.org/Vol-1973/paper01.pdf Way of finding: brute force 0 1 2 3 4 5 6 7 2 3 0 1 6 7 4 5 1 5 4 0 7 3 2 6 5 4 7 6 1 0 3 2 3 7 6 2 5 1 0 4 7 6 5 4 3 2 1 0 4 0 1 5 2 6 7 3 6 2 3 7 0 4 5 1 n=9, a(9)=333 Announcement 1: https://vk.com/wall162891802_1368, Eduard I. Vatutin, Natalia N. Nikitina, Maxim O. Manzuk, Sep 26 2020 (a(9)>=333) Announcement 2: https://vk.com/wall162891802_1485, Eduard I. Vatutin, Natalia N. Nikitina, Maxim O. Manzuk, Dec 07 2020 (a(9)=333) Way of finding: brute force using X-based fillings 0 1 2 3 4 5 6 7 8 7 8 4 0 6 1 2 3 5 4 3 1 2 8 7 5 6 0 1 6 7 5 3 4 0 8 2 5 4 0 8 7 2 3 1 6 8 2 3 1 0 6 7 5 4 3 5 6 7 2 8 4 0 1 6 0 8 4 5 3 1 2 7 2 7 5 6 1 0 8 4 3 n=10, a(10)>=890 Announcement: https://vk.com/wall162891802_1794, Eduard I. Vatutin, Nov 01 2021 Way of finding: expanding spectrum of diagonal transversals using loop rotation neighborhoods, diagonalizing 0 1 2 3 4 5 6 7 8 9 1 2 3 4 0 9 5 6 7 8 3 4 9 8 2 7 1 0 5 6 6 5 0 1 7 2 8 9 4 3 9 8 7 6 5 4 3 2 1 0 4 0 8 2 3 6 7 1 9 5 8 7 6 5 9 0 4 3 2 1 5 9 1 7 6 3 2 8 0 4 7 6 5 9 8 1 0 4 3 2 2 3 4 0 1 8 9 5 6 7 n=11, a(11)>=4828 Announcement: https://boinc.tbrada.eu/forum_thread.php?id=3104&postid=4149, Tomas Brada, Jul 09 2020 Way of finding: combinatorial structure from cyclic squares 0 1 2 3 4 5 6 7 8 9 10 1 2 3 5 6 9 7 10 0 4 8 7 10 8 0 3 1 5 9 6 2 4 3 5 9 4 10 6 8 0 2 7 1 4 6 7 10 1 8 2 3 9 0 5 5 9 4 6 8 7 0 1 3 10 2 10 8 0 1 5 2 9 4 7 3 6 6 7 10 8 2 0 3 5 4 1 9 8 0 1 2 9 3 4 6 10 5 7 2 3 5 9 7 4 10 8 1 6 0 9 4 6 7 0 10 1 2 5 8 3 n=12, a(12)>=30192 Announcement: https://vk.com/wall162891802_1732, Eduard I. Vatutin, Aug 18 2021 Way of finding: diagonalizing of known double Brown square (obtained using the composite squares method + diagonalizing) 0 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 9 8 11 5 10 0 6 7 5 8 10 6 11 4 1 3 9 7 0 2 11 7 5 8 10 2 9 1 3 6 4 0 7 5 8 10 6 3 0 2 4 11 9 1 9 0 1 2 3 7 10 11 5 4 8 6 6 11 7 5 8 1 4 0 2 10 3 9 10 6 11 7 5 0 3 9 1 8 2 4 3 4 9 0 1 6 5 10 11 2 7 8 2 3 4 9 0 10 7 8 6 1 11 5 4 9 0 1 2 11 8 6 7 3 5 10 8 10 6 11 7 9 2 4 0 5 1 3 n=13, a(13)>=131106 Announcement: https://boinc.tbrada.eu/forum_thread.php?id=3104&postid=4133, Tomas Brada, Jul 03 2020 Way of finding: cyclic squares 0 1 2 3 4 5 6 7 8 9 10 11 12 2 3 4 5 6 7 8 9 10 11 12 0 1 4 5 6 7 8 9 10 11 12 0 1 2 3 6 7 8 9 10 11 12 0 1 2 3 4 5 8 9 10 11 12 0 1 2 3 4 5 6 7 10 11 12 0 1 2 3 4 5 6 7 8 9 12 0 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 12 0 3 4 5 6 7 8 9 10 11 12 0 1 2 5 6 7 8 9 10 11 12 0 1 2 3 4 7 8 9 10 11 12 0 1 2 3 4 5 6 9 10 11 12 0 1 2 3 4 5 6 7 8 11 12 0 1 2 3 4 5 6 7 8 9 10 n=14, a(14)>=490218 Announcement: https://vk.com/wall162891802_2440, Eduard I. Vatutin, Jul 16 2023 Way of finding: full distributed diagonalizing of top (by transversals number) known DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 0 13 7 8 9 10 11 12 3 4 5 6 0 1 2 11 12 13 7 8 9 10 11 10 9 8 7 13 12 1 0 6 5 4 3 2 9 8 7 13 12 11 10 3 2 1 0 6 5 4 8 7 13 12 11 3 9 4 10 2 1 0 6 5 12 11 10 9 8 7 13 0 6 5 4 3 2 1 5 6 0 1 2 10 4 9 3 11 12 13 7 8 6 0 1 2 10 9 5 8 4 3 11 12 13 7 7 13 12 11 3 4 8 5 9 10 2 1 0 6 10 9 8 7 13 12 11 2 1 0 6 5 4 3 4 5 6 0 1 2 3 10 11 12 13 7 8 9 13 12 11 10 9 8 7 6 5 4 3 2 1 0 2 3 4 5 6 0 1 12 13 7 8 9 10 11 n=15, a(15)>=4620434 Announcement: https://vk.com/wall162891802_1910, Eduard I. Vatutin, Jan 25 2022 Way of finding: partial diagonalizing of cyclic LS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 0 4 5 3 7 13 9 14 11 12 10 6 8 10 11 12 13 6 7 1 2 4 5 9 14 8 0 3 13 6 7 14 8 9 4 5 12 10 0 1 2 3 11 5 3 4 10 11 12 14 8 1 2 7 13 6 9 0 12 10 11 7 13 6 0 1 3 4 8 9 14 2 5 3 4 5 11 12 10 8 9 2 0 13 6 7 14 1 6 7 13 8 9 14 5 3 10 11 1 2 0 4 12 14 8 9 1 2 0 12 10 7 13 3 4 5 11 6 4 5 3 12 10 11 9 14 0 1 6 7 13 8 2 8 9 14 2 0 1 10 11 13 6 4 5 3 12 7 2 0 1 5 3 4 13 6 14 8 12 10 11 7 9 11 12 10 6 7 13 2 0 5 3 14 8 9 1 4 7 13 6 9 14 8 3 4 11 12 2 0 1 5 10 9 14 8 0 1 2 11 12 6 7 5 3 4 10 13 n=16, a(16)>=32172800 Announcement: https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=109&postid=1201, Natalia Makarova, Jan 15 2021 Way of finding: composite squares method 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 3 2 1 0 7 6 5 4 11 10 9 8 15 14 13 12 1 0 3 2 5 4 7 6 9 8 11 10 13 12 15 14 2 3 0 1 6 7 4 5 10 11 8 9 14 15 12 13 12 13 14 15 8 9 10 11 4 5 6 7 0 1 2 3 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 13 12 15 14 9 8 11 10 5 4 7 6 1 0 3 2 14 15 12 13 10 11 8 9 6 7 4 5 2 3 0 1 4 5 6 7 0 1 2 3 12 13 14 15 8 9 10 11 7 6 5 4 3 2 1 0 15 14 13 12 11 10 9 8 5 4 7 6 1 0 3 2 13 12 15 14 9 8 11 10 6 7 4 5 2 3 0 1 14 15 12 13 10 11 8 9 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 11 10 9 8 15 14 13 12 3 2 1 0 7 6 5 4 9 8 11 10 13 12 15 14 1 0 3 2 5 4 7 6 10 11 8 9 14 15 12 13 2 3 0 1 6 7 4 5 n=17, a(17)>=204995269 Announcement: https://vk.com/wall162891802_1412, Eduard I. Vatutin, Oct 28 2020 Way of finding: cyclic square 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 1 4 5 6 7 8 9 10 11 12 13 14 15 16 0 1 2 3 6 7 8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 0 1 2 3 4 5 6 7 8 9 12 13 14 15 16 0 1 2 3 4 5 6 7 8 9 10 11 14 15 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 1 2 5 6 7 8 9 10 11 12 13 14 15 16 0 1 2 3 4 7 8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 7 8 11 12 13 14 15 16 0 1 2 3 4 5 6 7 8 9 10 13 14 15 16 0 1 2 3 4 5 6 7 8 9 10 11 12 15 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 n=18, a(18)>=281593874 Announcement: https://vk.com/wall162891802_1896, Eduard I. Vatutin, Jan 21 2022 Way of finding: Gergely method, expanding spectrum of diagonal transversals using intercalate and loop rotation neighborhoods 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 4 16 3 7 8 6 9 2 10 17 15 5 11 1 0 14 12 13 8 6 12 2 10 1 5 3 4 13 14 7 16 17 15 0 11 9 1 2 10 17 5 3 7 8 6 11 9 0 14 12 13 4 15 16 5 3 4 8 13 7 2 10 1 16 17 15 0 11 9 6 14 12 6 7 8 10 1 11 3 4 5 12 13 14 15 16 17 9 0 2 2 10 1 5 3 4 14 6 7 0 11 9 13 8 12 16 17 15 3 4 5 6 7 8 10 9 2 15 16 17 1 0 11 12 13 14 7 8 6 1 2 10 4 5 15 14 12 13 17 3 16 11 9 0 12 14 13 9 11 0 17 16 3 8 7 6 4 15 5 2 1 10 15 17 16 13 12 14 0 1 11 3 5 4 9 10 2 7 6 8 11 0 9 16 15 17 8 13 12 10 2 1 6 14 7 5 4 3 13 12 14 0 9 2 15 17 16 7 6 8 3 5 4 1 10 11 16 15 17 14 6 12 11 0 9 5 4 3 10 2 1 13 8 7 9 11 0 4 16 15 12 14 13 2 1 10 8 7 6 17 3 5 14 13 7 11 0 9 16 15 17 6 8 12 5 4 3 10 2 1 17 5 15 12 14 13 1 11 0 4 3 16 2 9 10 8 7 6 10 9 11 15 17 16 13 12 14 1 0 2 7 6 8 3 5 4 n=19, a(19)>=11254190082 Announcement: https://vk.com/wall162891802_1412, Eduard I. Vatutin, Oct 28 2020 Way of finding: cyclic square 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 n=20, a(20)>=90010806304 Announcement: https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=122&postid=1471, Natalia Makarova, Feb 13 2021 Way of finding: composite squares method 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2 3 4 0 1 7 8 9 5 6 12 13 14 10 11 17 18 19 15 16 4 0 1 2 3 9 5 6 7 8 14 10 11 12 13 19 15 16 17 18 1 2 3 4 0 6 7 8 9 5 11 12 13 14 10 16 17 18 19 15 3 4 0 1 2 8 9 5 6 7 13 14 10 11 12 18 19 15 16 17 15 16 17 18 19 10 11 12 13 14 5 6 7 8 9 0 1 2 3 4 17 18 19 15 16 12 13 14 10 11 7 8 9 5 6 2 3 4 0 1 19 15 16 17 18 14 10 11 12 13 9 5 6 7 8 4 0 1 2 3 16 17 18 19 15 11 12 13 14 10 6 7 8 9 5 1 2 3 4 0 18 19 15 16 17 13 14 10 11 12 8 9 5 6 7 3 4 0 1 2 5 6 7 8 9 0 1 2 3 4 15 16 17 18 19 10 11 12 13 14 7 8 9 5 6 2 3 4 0 1 17 18 19 15 16 12 13 14 10 11 9 5 6 7 8 4 0 1 2 3 19 15 16 17 18 14 10 11 12 13 6 7 8 9 5 1 2 3 4 0 16 17 18 19 15 11 12 13 14 10 8 9 5 6 7 3 4 0 1 2 18 19 15 16 17 13 14 10 11 12 10 11 12 13 14 15 16 17 18 19 0 1 2 3 4 5 6 7 8 9 12 13 14 10 11 17 18 19 15 16 2 3 4 0 1 7 8 9 5 6 14 10 11 12 13 19 15 16 17 18 4 0 1 2 3 9 5 6 7 8 11 12 13 14 10 16 17 18 19 15 1 2 3 4 0 6 7 8 9 5 13 14 10 11 12 18 19 15 16 17 3 4 0 1 2 8 9 5 6 7 n=21, a(21)>=51162162017 Announcement: https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=122&postid=1481, Natalia Makarova, Feb 20 2021 Way of finding: ? 0 12 3 2 17 19 20 18 13 15 16 14 1 8 10 11 9 4 6 7 5 2 1 0 12 20 18 17 19 16 14 13 15 3 11 9 8 10 7 5 4 6 12 3 2 1 18 20 19 17 14 16 15 13 0 9 11 10 8 5 7 6 4 1 0 12 3 19 17 18 20 15 13 14 16 2 10 8 9 11 6 4 5 7 8 10 11 9 4 12 7 6 0 2 3 1 5 17 19 20 18 13 15 16 14 11 9 8 10 6 5 4 12 3 1 0 2 7 20 18 17 19 16 14 13 15 9 11 10 8 12 7 6 5 1 3 2 0 4 18 20 19 17 14 16 15 13 10 8 9 11 5 4 12 7 2 0 1 3 6 19 17 18 20 15 13 14 16 17 19 20 18 13 15 16 14 8 12 11 10 9 4 6 7 5 0 2 3 1 20 18 17 19 16 14 13 15 10 9 8 12 11 7 5 4 6 3 1 0 2 18 20 19 17 14 16 15 13 12 11 10 9 8 5 7 6 4 1 3 2 0 19 17 18 20 15 13 14 16 9 8 12 11 10 6 4 5 7 2 0 1 3 3 2 1 0 7 6 5 4 11 10 9 8 12 16 15 14 13 20 19 18 17 4 6 7 5 0 2 3 1 17 19 20 18 14 13 12 16 15 8 10 11 9 7 5 4 6 3 1 0 2 20 18 17 19 16 15 14 13 12 11 9 8 10 5 7 6 4 1 3 2 0 18 20 19 17 13 12 16 15 14 9 11 10 8 6 4 5 7 2 0 1 3 19 17 18 20 15 14 13 12 16 10 8 9 11 13 15 16 14 8 10 11 9 4 6 7 5 18 0 2 3 1 17 12 20 19 16 14 13 15 11 9 8 10 7 5 4 6 20 3 1 0 2 19 18 17 12 14 16 15 13 9 11 10 8 5 7 6 4 17 1 3 2 0 12 20 19 18 15 13 14 16 10 8 9 11 6 4 5 7 19 2 0 1 3 18 17 12 20 n=22, a(22)>=3227747329246 Announcement: https://boinc.multi-pool.info/latinsquares/forum_thread.php?id=122&postid=1601, Natalia Makarova, Mar 09 2021 Way of finding: ? 1 13 3 4 5 6 7 8 9 10 11 0 21 20 19 18 17 16 15 14 2 12 2 3 15 5 6 7 8 9 10 11 1 12 0 21 20 19 18 17 16 4 14 13 3 4 5 17 7 8 9 10 11 1 2 13 12 0 21 20 19 18 6 16 15 14 4 5 6 7 19 9 10 11 1 2 3 14 13 12 0 21 20 8 18 17 16 15 5 6 7 8 9 21 11 1 2 3 4 15 14 13 12 0 10 20 19 18 17 16 6 7 8 9 10 11 12 2 3 4 5 16 15 14 13 1 0 21 20 19 18 17 7 8 9 10 11 1 2 14 4 5 6 17 16 15 3 13 12 0 21 20 19 18 8 9 10 11 1 2 3 4 16 6 7 18 17 5 15 14 13 12 0 21 20 19 9 10 11 1 2 3 4 5 6 18 8 19 7 17 16 15 14 13 12 0 21 20 10 11 1 2 3 4 5 6 7 8 20 9 19 18 17 16 15 14 13 12 0 21 0 1 2 3 4 5 6 7 8 9 10 21 20 19 18 17 16 15 14 13 12 11 21 0 12 13 14 15 16 17 18 19 9 20 8 7 6 5 4 3 2 1 11 10 20 21 0 12 13 14 15 16 17 7 19 8 18 6 5 4 3 2 1 11 10 9 19 20 21 0 12 13 14 15 5 17 18 7 6 16 4 3 2 1 11 10 9 8 18 19 20 21 0 12 13 3 15 16 17 6 5 4 14 2 1 11 10 9 8 7 17 18 19 20 21 0 1 13 14 15 16 5 4 3 2 12 11 10 9 8 7 6 16 17 18 19 20 10 0 12 13 14 15 4 3 2 1 11 21 9 8 7 6 5 15 16 17 18 8 20 21 0 12 13 14 3 2 1 11 10 9 19 7 6 5 4 14 15 16 6 18 19 20 21 0 12 13 2 1 11 10 9 8 7 17 5 4 3 13 14 4 16 17 18 19 20 21 0 12 1 11 10 9 8 7 6 5 15 3 2 12 2 14 15 16 17 18 19 20 21 0 11 10 9 8 7 6 5 4 3 13 1 11 12 13 14 15 16 17 18 19 20 21 10 9 8 7 6 5 4 3 2 1 0 Jul 16 2023