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Srinivasa Ramanujan (1887-1920) was a largely self-taught mathematician from India, some of whose results still inspire research today. Once, when ill in the hospital in England, he was visited by fellow mathematician G. H. Hardy (1877-1947), who later wrote:
I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."
Using one copy each of the digits 1, 7, 2, and 9, and any standard operations, create each of the positive integers. All four numbers must be used, but no others. Your solutions will be assigned an exquisiteness level.
Use the online submissions page to get your Integermania solutions posted here! This problem is now in semi-retired status, so you may submit an unlimited number of solutions each month.
Page 1 (1-400), Page 2 (401-800), Page 3 (801-1200), Page 4 (1201-4000), Page 11 (4001+).
| 801 (2.2) $\dfrac{72}{9\%} + 1$ Jonathan Frank, 4/22 Rye, NY |
802 (2.4) $\dfrac{7.\overline{9}}{1\%} + 2$ Steve Wilson, 6/22 Lawrence, KS |
803 (3.2) $\dfrac{9^2}{.1} - 7$ Steve Wilson, 6/22 Lawrence, KS |
804 (3.6) $((\sqrt{9})!)! + 7 \times 12$ Steve Wilson, 6/22 Lawrence, KS |
805 (2.2) $\dfrac{9 + 7.1}{2\%}$ Steve Wilson, 6/22 Lawrence, KS |
806 (4.2) $\dfrac{1.\overline{7}}{.\overline{2}\%} + (\sqrt{9})!$ Steve Wilson, 6/22 Lawrence, KS |
807 (3.4) $\dfrac{2^{\sqrt{9}}}{1\%} + 7$ Steve Wilson, 6/22 Lawrence, KS |
808 (4.0) $(.\overline{1}\%)^{-2}\pm - 9 + 7$ Steve Wilson, 6/22 Lawrence, KS |
809 (2.8) $\dfrac{1.\overline{7}}{.\overline{2}\%} + 9$ Steve Wilson, 6/22 Lawrence, KS |
810 (2.2) $(7 + 2) \times \dfrac{9}{.1}$ Steve Wilson, 6/22 Lawrence, KS |
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| 811 (3.6) $((\sqrt{7 + 2})!)! + 91$ Steve Wilson, 6/22 Lawrence, KS |
812 (3.2) $(7 - 1)! + 92$ Steve Wilson, 6/22 Lawrence, KS |
813 (3.2) $271 \times \sqrt{9}$ Steve Wilson, 6/22 Lawrence, KS |
814 (4.2) $(.\overline{1}\%)^{-2}\pm + 7 - \sqrt{9}$ Steve Wilson, 4/23 Lawrence, KS |
815 (2.6) $\dfrac{1 + 9 \times 7\%}{.2\%}$ Steve Wilson, 6/22 Lawrence, KS |
816 (4.2) $\dfrac{.9}{.\overline{1}\%} + (\sqrt{7 + 2})!$ Steve Wilson, 6/22 Lawrence, KS |
817 (3.2) $\dfrac{9^2}{.1} + 7$ Steve Wilson, 6/22 Lawrence, KS |
818 (4.2) $(.\overline{1}\%)^{-2}\pm + 7.\overline{9}$ Steve Wilson, 4/23 Lawrence, KS |
819 (2.0) $91 \times (7 + 2)$ Steve Wilson, 6/22 Lawrence, KS |
820 (2.6) $\dfrac{7 + 1.2}{.\overline{9}\%}$ Steve Wilson, 6/22 Lawrence, KS |
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| 821 (2.4) $\dfrac{92}{.\overline{1}} - 7$ Steve Wilson, 6/22 Lawrence, KS |
823 (3.0) $\dfrac{.9\overline{2}}{.\overline{1}\%} - 7$ Steve Wilson, 4/23 Lawrence, KS |
824 (2.8) $\dfrac{.9}{.\overline{1}\%} + 7 \times 2$ Steve Wilson, 6/22 Lawrence, KS |
826 (4.0) $(.\overline{1}\%)^{-2}\pm + 9 + 7$ Steve Wilson, 4/23 Lawrence, KS |
828 (2.2) $\dfrac{9}{1\%} - 72$ Jonathan Frank, 2/22 Rye, NY |
830 (2.4) $\dfrac{2 + 9 \times .7}{1\%}$ Steve Wilson, 6/22 Lawrence, KS |
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| 831 (3.4) $7 \times \left( \dfrac{1}{.2} \right)! - 9$ Steve Wilson, 4/23 Lawrence, KS |
832 (2.4) $\dfrac{9 - .7}{1\%} + 2$ Steve Wilson, 6/22 Lawrence, KS |
834 (3.8) $7 \times \left( \dfrac{1}{.2} \right)! - (\sqrt{9})!$ Steve Wilson, 4/23 Lawrence, KS |
835 (2.4) $\dfrac{92}{.\overline{1}} + 7$ Steve Wilson, 6/22 Lawrence, KS |
837 (2.8) $\dfrac{.9}{.\overline{1}\%} + 27$ Steve Wilson, 6/22 Lawrence, KS |
838 (3.6) $\dfrac{7!}{(\sqrt{9})!} - 2 \times 1$ Steve Wilson, 4/23 Lawrence, KS |
839 (3.4) $\dfrac{7!}{(\sqrt[2]{9})!} - 1$ Steve Wilson, 4/23 Lawrence, KS |
840 (2.6) $\dfrac{7 \times 1.2}{.\overline{9}\%}$ Steve Wilson, 6/22 Lawrence, KS |
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| 841 (2.2) $\dfrac{17}{2\%} - 9$ Jonathan Frank, 4/22 Rye, NY |
842 (3.6) $\dfrac{7!}{(\sqrt{9})!} + 2 \times 1$ Steve Wilson, 4/23 Lawrence, KS |
843 (3.4) $\dfrac{1}{2\pmf} + 7^{\sqrt{9}}$ Steve Wilson, 6/22 Lawrence, KS |
844 (3.6) $\dfrac{17}{2\%} - (\sqrt{9})!$ Jonathan Frank, 2/22 Rye, NY |
845 (3.0) $\dfrac{.9}{.\overline{1}\%} + \dfrac{7}{.2}$ Steve Wilson, 6/22 Lawrence, KS |
846 (3.8) $7 \times \left( \dfrac{1}{.2} \right)! + (\sqrt{9})!$ Steve Wilson, 4/23 Lawrence, KS |
847 (3.4) $\dfrac{17}{2\%} - \sqrt{9}$ Jonathan Frank, 8/21 Rye, NY |
848 (2.6) $\dfrac{1.9}{.\overline{2}\%} - 7$ Steve Wilson, 6/22 Lawrence, KS |
849 (2.6) $\dfrac{17}{2\%} - .\overline{9}$ Steve Wilson, 6/22 Lawrence, KS |
850 (2.2) $\dfrac{9 + 7 + 1}{2\%}$ Steve Wilson, 6/22 Lawrence, KS |
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| 851 (2.6) $\dfrac{17}{2\%} + .\overline{9}$ Steve Wilson, 6/22 Lawrence, KS |
852 (3.6) $\dfrac{7!}{(\sqrt{9})!} + 12$ Steve Wilson, 4/23 Lawrence, KS |
853 (3.4) $\dfrac{17}{2\%} + \sqrt{9}$ Jonathan Frank, 5/22 Rye, NY |
855 (2.4) $\dfrac{97 - 2}{.\overline{1}}$ Steve Wilson, 6/22 Lawrence, KS |
856 (3.6) $\dfrac{17}{2\%} + (\sqrt{9})!$ Jonathan Frank, 5/22 Rye, NY |
857 (3.6) $\sqrt[ \sqrt{.\overline{1}}]{9} + 2^7$ Steve Wilson, 6/22 Lawrence, KS |
859 (2.2) $\dfrac{17}{2\%} + 9$ Jonathan Frank, 5/22 Rye, NY |
860 (3.8) $\dfrac{7!}{(\sqrt{9})!} + \dfrac{2}{.1}$ Steve Wilson, 4/23 Lawrence, KS |
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| 861 (3.6) $\dfrac{7!}{(\sqrt{9})!} + 21$ Steve Wilson, 4/23 Lawrence, KS |
862 (2.6) $\dfrac{1.9}{.\overline{2}\%} + 7$ Steve Wilson, 6/22 Lawrence, KS |
865 (2.4) $\dfrac{9}{1\%} - \dfrac{7}{.2}$ Steve Wilson, 6/22 Lawrence, KS |
866 (2.4) $\dfrac{7}{(1 - .2)\%} - 9$ Steve Wilson, 6/22 Lawrence, KS |
867 (3.2) $17^2 \times \sqrt{9}$ Hannah Maleki, 11/16 Overland Park, KS |
869 (3.8) $\dfrac{7}{(1 - .2)\%} - (\sqrt{9})!$ Steve Wilson, 6/22 Lawrence, KS |
870 (3.6) $\dfrac{2^{\sqrt{9}} + .7}{1\%}$ Steve Wilson, 6/22 Lawrence, KS |
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| 871 (2.4) $\dfrac{97}{.\overline{1}} - 2$ Steve Wilson, 6/22 Lawrence, KS |
872 (3.6) $\dfrac{7}{(1 - .2)\%} - \sqrt{9}$ Steve Wilson, 6/22 Lawrence, KS |
873 (2.2) $\dfrac{9}{1\%} - 27$ Jonathan Frank, 5/22 Rye, NY |
874 (2.8) $\dfrac{7}{(1 - .2)\%} - .\overline{9}$ Steve Wilson, 6/22 Lawrence, KS |
875 (2.4) $\dfrac{97}{.\overline{1}} + 2$ Steve Wilson, 6/22 Lawrence, KS |
876 (2.8) $\dfrac{7}{(1 - .2)\%} + .\overline{9}$ Steve Wilson, 6/22 Lawrence, KS |
877 (2.6) $\dfrac{.7}{(9 - 1)\%\%} + 2$ Steve Wilson, 6/22 Lawrence, KS |
878 (3.6) $\dfrac{7}{(1 - .2)\%} + \sqrt{9}$ Steve Wilson, 6/22 Lawrence, KS |
880 (2.4) $\dfrac{7 + 9 \times .2}{1\%}$ Steve Wilson, 6/22 Lawrence, KS |
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| 881 (3.8) $\dfrac{7}{(1 - .2)\%} - (\sqrt{9})!$ Steve Wilson, 6/22 Lawrence, KS |
882 (2.8) $\dfrac{.9}{.\overline{1}\%} + 72$ Steve Wilson, 6/22 Lawrence, KS |
884 (2.4) $\dfrac{7}{(1 - .2)\%} + 9$ Steve Wilson, 6/22 Lawrence, KS |
886 (2.2) $\dfrac{9}{1\%} - 7 \times 2$ Jonathan Frank, 3/22 Rye, NY |
887 (2.4) $\dfrac{9 - .2}{1\%} + 7$ Steve Wilson, 6/22 Lawrence, KS |
889 (4.0) $(.\overline{1}\%)^{-2}\pm + 79$ Steve Wilson, 6/22 Lawrence, KS |
890 (2.8) $\dfrac{1.9\overline{7}}{.\overline{2}\%}$ Steve Wilson, 6/22 Lawrence, KS |
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| 891 (2.2) $\dfrac{9}{1\%} - 7 - 2$ Jonathan Frank, 3/22 Rye, NY |
893 (2.2) $\dfrac{9}{(2 - 1)\%} - 7$ Steve Wilson, 6/22 Lawrence, KS |
894 (3.6) $\dfrac{9}{1\%} - (\sqrt{7 + 2})!$ Steve Wilson, 6/22 Lawrence, KS |
895 (2.2) $\dfrac{179}{.2}$ Jonathan Frank, 3/22 Rye, NY |
897 (3.4) $\dfrac{9}{1\%} - \sqrt{7 + 2}$ Jonathan Frank, 5/22 Rye, NY |
898 (3.2) $\dfrac{9}{1^7 \%} - 2$ Steve Wilson, 6/22 Lawrence, KS |
899 (2.6) $\dfrac{7 + 2}{1\%} - .\overline{9}$ Steve Wilson, 6/22 Lawrence, KS |
900 (2.2) $\dfrac{2}{\left(1 - \dfrac79 \right)\%}$ Steve Wilson, 6/22 Lawrence, KS |
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| 901 (2.6) $\dfrac{7 + 2}{1\%} + .\overline{9}$ Steve Wilson, 6/22 Lawrence, KS |
902 (3.2) $\dfrac{9}{1^7 \%} + 2$ Steve Wilson, 6/22 Lawrence, KS |
903 (2.0) $129 \times 7$ Bing Guo, 11/13 Lawrence, KS |
905 (2.0) $912 - 7$ Emily Boudville, 6/13 Perth, Western Australia |
906 (3.6) $\dfrac{7 + 2}{1\%} + (\sqrt{9})!$ Steve Wilson, 6/22 Lawrence, KS |
907 (2.2) $\dfrac{9}{(2 - 1)\%} + 7$ Steve Wilson, 6/22 Lawrence, KS |
908 (3.8) $(.1)^{-7} \%\% - 92$ Steve Wilson, 6/22 Lawrence, KS |
909 (2.2) $\dfrac{9}{1\%} + 7 + 2$ Jonathan Frank, 4/22 Rye, NY |
910 (2.6) $\dfrac{7 + 2.1}{.\overline{9}\%}$ Steve Wilson, 6/22 Lawrence, KS |
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| 913 (2.2) $\dfrac{9.2}{1\%} - 7$ Steve Wilson, 6/22 Lawrence, KS |
914 (2.0) $921 - 7$ Bing Guo, 10/13 Lawrence, KS |
915 (2.0) $917 - 2$ Steve Wilson, 6/22 Lawrence, KS |
917 (3.4) $7! \times .2 - 91$ Steve Wilson, 6/22 Lawrence, KS |
918 (3.6) $7! \times .2 - \dfrac{9}{.1}$ Steve Wilson, 6/22 Lawrence, KS |
919 (2.0) $912 + 7$ Steve Wilson, 8/13 Lawrence, KS |
920 (3.2) $\dfrac{9.2}{1^7 \%}$ Steve Wilson, 6/22 Lawrence, KS |
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| 921 (3.6) $\sqrt{ (1\pm) ^{-2} \phantom8} - 79$ Steve Wilson, 6/22 Lawrence, KS |
923 (2.8) $\dfrac{9.\overline{2}}{1\%} + .\overline{7}$ Steve Wilson, 6/22 Lawrence, KS |
925 (4.0) $\dfrac{((\sqrt{9})!)! + 1}{.\overline{7}} - 2$ Steve Wilson, 4/23 Lawrence, KS |
926 (2.0) $927 - 1$ Giuseppe Favacchio, 4/13 Scicli, Italy |
927 (2.0) $927 \times 1$ Sophie Fischer & Violet McCabe, 4/13 New York, NY |
928 (2.0) $927 + 1$ Giuseppe Favacchio, 4/13 Scicli, Italy |
929 (4.0) $\dfrac{((\sqrt{9})!)! + 1}{.\overline{7}} + 2$ Steve Wilson, 4/23 Lawrence, KS |
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| 931 (3.0) $7^2 \times 19$ Hyun Cheong, 2/14 Overland Park, KS |
935 (2.4) $\dfrac{9 + \dfrac{.7}{2}}{1\%}$ Steve Wilson, 6/22 Lawrence, KS |
937 (3.6) $\sqrt{ (1 \pm)^{-2} \phantom8} - 9 \times 7$ Steve Wilson, 6/22 Lawrence, KS |
938 (3.8) $\dfrac{.9}{.\overline{1}\%} + 2^7$ Steve Wilson, 6/22 Lawrence, KS |
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| 943 (2.2) $\dfrac{19}{2\%} - 7$ Jonathan Frank, 6/22 Rye, NY |
945 (2.6) $\dfrac{9.1 - 7}{.\overline{2}\%}$ Steve Wilson, 6/22 Lawrence, KS |
948 (2.0) $79 \times 12$ Allison Layne-Mulhern, 10/13 Leawood, KS |
949 (3.2) $\dfrac{9}{1\%} + 7^2$ Jonathan Frank, 10/21 Rye, NY |
950 (2.2) $\dfrac{97 - 2}{.1}$ Steve Wilson, 6/22 Lawrence, KS |
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| 951 (3.6) $\dfrac{.\overline{9}}{1\pmf} - 7^2$ Steve Wilson, 6/22 Lawrence, KS |
957 (2.2) $\dfrac{19}{2\%} + 7$ Jonathan Frank, 6/22 Rye, NY |
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| 961 (3.2) $\sqrt[.1]{2} - 7 \times 9$ Steve Wilson, 6/22 Lawrence, KS |
963 (3.4) $\left( (.1)^{-2} + 7 \right) \times 9$ Steve Wilson, 6/22 Lawrence, KS |
965 (2.8) $\dfrac{1.\overline{9} - 7\%}{.2\%}$ Steve Wilson, 6/22 Lawrence, KS |
968 (2.2) $\dfrac{97}{.1} - 2$ Margaret Wilson, 4/13 Atlanta, GA |
969 (2.0) $971 - 2$ D.J. Demjanik, 12/13 Shawnee, KS |
970 (2.2) $\dfrac{9.7}{(2 - 1)\%}$ Steve Wilson, 6/22 Lawrence, KS |
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| 971 (2.0) $972 - 1$ Edie Abraham-Macht, 4/13 Brooklyn, NY |
972 (2.0) $\dfrac{972}{1}$ Edie Abraham-Macht, 4/13 Brooklyn, NY |
973 (2.0) $972 + 1$ Giuseppe Favacchio, 4/13 Scicli, Italy |
978 (2.8) $\dfrac{9.\overline{7}}{1\%} + .\overline{2}$ Steve Wilson, 6/22 Lawrence, KS |
979 (3.8) $\sqrt{ (1\pm)^{-2} \phantom8} - 7 \times \sqrt{9}$ Steve Wilson, 6/22 Lawrence, KS |
980 (3.8) $\dfrac{.\overline{9} - 2\%}{1^7 \pmf}$ Steve Wilson, 4/23 Lawrence, KS |
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| 982 (3.8) $(.1)^{-7} \%\% - 9 \times 2$ Steve Wilson, 6/22 Lawrence, KS |
983 (2.8) $\dfrac{2 - .9}{.\overline{1}\%} - 7$ Steve Wilson, 6/22 Lawrence, KS |
984 (3.6) $\sqrt{ (1\pm)^{-2} \phantom8} - 7 - 9$ Steve Wilson, 6/22 Lawrence, KS |
985 (2.2) $\dfrac{197}{.2}$ Jonathan Frank, 6/22 Rye, NY |
986 (2.8) $\dfrac{.\overline{9}}{.1\%} - 2 \times 7$ Steve Wilson, 6/22 Lawrence, KS |
987 (3.0) $\dfrac{.\overline{9} - 2\%}{.1\%} + 7$ Steve Wilson, 4/23 Lawrence, KS |
989 (3.4) $7! \times .2 - 19$ Steve Wilson, 6/22 Lawrence, KS |
990 (2.2) $\dfrac{7.9 + 2}{1\%}$ Steve Wilson, 6/22 Lawrence, KS |
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| 991 (2.8) $\dfrac{.\overline{9}}{.1\%} - 7 - 2$ Steve Wilson, 6/22 Lawrence, KS |
992 (3.8) $\sqrt{ (1\pm)^{-2} \phantom8} - 7.\overline{9}$ Steve Wilson, 6/22 Lawrence, KS |
993 (2.6) $\dfrac{1.\overline{9}}{.2\%} - 7$ Steve Wilson, 6/22 Lawrence, KS |
994 (4.0) $\sqrt{ (1\pm)^{-2} \phantom8} - 7 + .\overline{9}$ Steve Wilson, 6/22 Lawrence, KS |
995 (2.6) $\dfrac{9 - 7 - 1\%}{.2\%}$ Steve Wilson, 6/22 Lawrence, KS |
996 (3.8) $\sqrt{ (1\pm)^{-2} \phantom8} - 7 + \sqrt{9}$ Steve Wilson, 6/22 Lawrence, KS |
997 (2.8) $\dfrac{2 - .9}{.\overline{1}\%} + 7$ Steve Wilson, 6/22 Lawrence, KS |
998 (3.4) $7! \times .2 - 9 - 1$ Steve Wilson, 6/22 Lawrence, KS |
999 (2.4) $\dfrac{7 + 2}{.9\%} - 1$ Steve Wilson, 6/22 Lawrence, KS |
1000 (2.4) $\dfrac{7 + 2 \times 1}{.9\%}$ Steve Wilson, 6/22 Lawrence, KS |
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| 1024 (3.0) $2^7 \times (9 - 1)$ Gregory Bayer, 3/20 Sydney, NSW |
1029 (3.2) $7^{2+1} \times \sqrt{9}$ Gregory Bayer, 3/20 Sydney, NSW |
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| 1079 (3.2) $(7 - 2)! \times 9 - 1$ Gregory Bayer, 11/19 Sydney, NSW |
1080 (3.4) $(7 - 1)! \times \dfrac{ \sqrt{9}}{2}$ Gregory Bayer, 3/20 Sydney, New South Wales |
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| 1081 (3.2) $(7 - 2)! \times 9 + 1$ Jonathan Frank, 5/21 Rye, NY |
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| 1119 (3.2) $7! \times \dfrac29 - 1$ Ashlyn Howatson, 4/13 Perth, Western Australia |
1120 (3.2) $7! \times \dfrac29 \times 1$ Parker Thomsen, 5/15 Lenexa, KS |
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| 1121 (3.2) $7! \times \dfrac29 + 1$ Parker Thomsen, 5/15 Lenexa, KS |
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| 1143 (2.0) $127 \times 9$ Bing Guo, 11/13 Lawrence, KS |
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| 1151 (3.0) $2^7 \times 9 - 1$ Sierra Henricks, 4/14 Olathe, KS |
1152 (3.0) $2^7 \times 9^1$ Hannah Maleki, 9/16 Overland Park, KS |
1153 (3.0) $2^7 \times 9 + 1$ Iris Behm, 1/14 Lenexa, KS |
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| 1164 (2.0) $97 \times 12$ Allison Layne-Mulhern, 11/13 Leawood, KS |
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| 1176 (3.4) $( \sqrt{9} + 1)! \times 7^2$ Gregory Bayer, 3/20 Sydney, NSW |
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| 1199 (3.6) $\dfrac{72}{(\sqrt{9})!\%} - 1$ Jonathan Frank, 6/22 Rye, NY |
1200 (3.6) $\dfrac{72}{(\sqrt{9})!\%} \times 1$ Jonathan Frank, 6/22 Rye, NY |
Page 1 (1-400), Page 2 (401-800), Page 3 (801-1200), Page 4 (1201-4000), Page 11 (4001+).