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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+).
| 1201 (3.6) $\dfrac{72}{(\sqrt{9})!\%} + 1$ Jonathan Frank, 6/22 Rye, NY |
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| 1212 (3.2) $\dfrac{7}{1\%} + 2^9$ Jonathan Frank, 6/22 Rye, NY |
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| 1260 (2.2) $\dfrac{9 \times 2 \times 7}{.1}$ Margaret Wilson, 4/13 Atlanta, GA |
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| 1274 (2.0) $91 \times 7 \times 2$ Allison Layne-Mulhern, 10/13 Leawood, KS |
1279 (2.0) $1279$ Ethan L., 4/13 New York, NY |
1280 (3.0) $2^7 \times (9 + 1)$ Gregory Bayer, 4/20 Sydney, NSW |
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| 1297 (2.0) $1297$ Garrett Donnelly, 5/13 Atlanta, GA |
1298 (2.2) $\dfrac{91}{7\%} - 2$ Jonathan Frank, 6/22 Rye, NY |
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| 1302 (2.2) $\dfrac{91}{7\%} + 2$ Jonathan Frank, 6/22 Rye, NY |
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| 1323 (2.0) $7 \times 9 \times 21$ Kendra Stindt, 8/13 Topeka, KS |
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| 1344 (2.0) $192 \times 7$ Echo Anderson, 11/13 Lenexa, KS |
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| 1368 (2.0) $72 \times 19$ Justin Keck, 3/17 Lawrence, KS |
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| 1377 (3.0) $9^2 \times 17$ Deborah Kangas, 1/14 Lenexa, KS |
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| 1391 (3.2) $2 \times \dfrac{7}{1\%} - 9$ Jonathan Frank, 8/21 Rye, NY |
1397 (3.4) $2 \times \dfrac{7}{1\%} - \sqrt{9}$ Jonathan Frank, 8/21 Rye, NY |
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| 1403 (3.4) $2 \times \dfrac{7}{1\%} + \sqrt{9}$ Jonathan Frank, 8/21 Rye, NY |
1409 (3.2) $2 \times \dfrac{7}{1\%} + 9$ Jonathan Frank, 8/21 Rye, NY |
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| 1429 (3.4) $\dfrac{\sqrt{9}}{2\pmf} - 71$ Jonathan Frank, 7/22 Rye, NY |
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| 1438 (2.0) $719 \times 2$ D.J. Demjanik, 12/13 Shawnee, KS |
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| 1483 (3.4) $\dfrac{\sqrt{9}}{2\pmf} - 17$ Jonathan Frank, 7/22 Rye, NY |
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| 1492 (3.4) $\dfrac{\sqrt{9}}{2\pmf} - 7 - 1$ Jonathan Frank, 7/22 Rye, NY |
1493 (3.4) $\dfrac{\sqrt{9}}{2\pmf} - 7 \times 1$ Jonathan Frank, 7/22 Rye, NY |
1494 (3.4) $\dfrac{\sqrt{9}}{2\pmf} - 7 + 1$ Jonathan Frank, 7/22 Rye, NY |
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| 1506 (3.4) $\dfrac{\sqrt{9}}{2\pmf} + 7 - 1$ Jonathan Frank, 7/22 Rye, NY |
1507 (3.4) $\dfrac{\sqrt{9}}{2\pmf} + 7 \times 1$ Jonathan Frank, 7/22 Rye, NY |
1508 (3.4) $\dfrac{\sqrt{9}}{2\pmf} + 7 + 1$ Jonathan Frank, 7/22 Rye, NY |
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| 1517 (3.4) $\dfrac{\sqrt{9}}{2\pmf} + 17$ Jonathan Frank, 7/22 Rye, NY |
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| 1548 (2.0) $172 \times 9$ Allison Layne-Mulhern, 11/13 Leawood, KS |
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| 1564 (2.0) $17 \times 92$ Echo Anderson, 12/13 Lenexa, KS |
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| 1571 (3.4) $\dfrac{\sqrt{9}}{2\pmf} + 71$ Jonathan Frank, 7/22 Rye, NY |
1580 (2.2) $79 \times \dfrac{2}{.1}$ D.J. Demjanik, 9/13 Shawnee, KS |
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| 1582 (2.0) $791 \times 2$ D.J. Demjanik, 12/13 Shawnee, KS |
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| 1659 (2.0) $79 \times 21$ D.J. Demjanik, 9/13 Shawnee, KS |
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| 1680 (3.2) $\dfrac{7!}{9} \times (2 + 1)$ Jonathan Frank, 7/21 Rye, NY |
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| 1729 (2.0) $1729$ Scott Thibodeaux, 4/13 Denver, CO |
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| 1792 (2.0) $1792$ Sara Fridovich-Keil, 6/13 Decatur, GA |
1793 (2.2) $\dfrac{9}{1\%} \times 2 - 7$ Jonathan Frank, 9/21 Rye, NY |
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| 1807 (2.2) $\dfrac{9}{1\%} \times 2 + 7$ Jonathan Frank, 9/21 Rye, NY |
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| 1834 (2.0) $917 \times 2$ D.J. Demjanik, 12/13 Shawnee, KS |
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| 1903 (2.4) $\dfrac{2}{.1\%} - 97$ Jonathan Frank, 6/22 Rye, NY |
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| 1921 (2.4) $\dfrac{2}{.1\%} - 79$ Jonathan Frank, 6/22 Rye, NY |
1927 (2.0) $1927$ Sara Fridovich-Keil, 6/13 Decatur, GA |
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| 1937 (2.4) $\dfrac{2}{.1\%} - 7 \times 9$ Jonathan Frank, 6/22 Rye, NY |
1940 (2.2) $\dfrac{97}{.1} \times 2$ Margaret Wilson, 4/13 Atlanta, GA |
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| 1942 (2.0) $971 \times 2$ Kendra Stindt, 11/13 Topeka, KS |
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| 1953 (2.0) $217 \times 9$ Alicia Kasper, 10/13 Cranbury, NJ |
1958 (3.6) $\dfrac{2}{1\pmf} - 7 \times (\sqrt{9})!$ Jonathan Frank, 6/22 Rye, NY |
1960 (3.4) $\dfrac{7}{1\pmf} - (9 - 2)!$ Jonathan Frank, 6/22 Rye, NY |
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| 1972 (2.0) $1972$ Sara Fridovich-Keil, 6/13 Decatur, GA |
1979 (3.4) $\dfrac{2}{1\pmf} - 7 \times \sqrt{9}$ Jonathan Frank, 6/22 Rye, NY |
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| 1984 (2.4) $\dfrac{2}{.1\%} - 7 - 9$ Jonathan Frank, 6/22 Rye, NY |
1987 (3.6) $\dfrac{2}{1\pmf} - 7 - (\sqrt{9})!$ Jonathan Frank, 6/22 Rye, NY |
1990 (3.4) $\dfrac{2}{1\pmf} - 7 - \sqrt{9}$ Jonathan Frank, 6/22 Rye, NY |
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| 1996 (3.4) $\dfrac{2}{1\pmf} - 7 + \sqrt{9}$ Jonathan Frank, 6/22 Rye, NY |
1998 (2.4) $\dfrac{2}{.1\%} + 7 - 9$ Jonathan Frank, 6/22 Rye, NY |
1999 (3.6) $\dfrac{2}{1\pmf} - 7 + (\sqrt{9})!$ Jonathan Frank, 6/22 Rye, NY |
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| 2001 (3.6) $\dfrac{2}{1\pmf} + 7 - (\sqrt{9})!$ Jonathan Frank, 6/22 Rye, NY |
2002 (2.4) $\dfrac{2}{.1\%} - 7 + 9$ Jonathan Frank, 6/22 Rye, NY |
2004 (3.4) $\dfrac{2}{1\pmf} + 7 - \sqrt{9}$ Jonathan Frank, 6/22 Rye, NY |
2010 (3.4) $\dfrac{2}{1\pmf} + 7 + \sqrt{9}$ Jonathan Frank, 6/22 Rye, NY |
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| 2013 (3.6) $\dfrac{2}{1\pmf} + 7 + (\sqrt{9})!$ Jonathan Frank, 6/22 Rye, NY |
2016 (2.4) $\dfrac{2}{.1\%} + 7 + 9$ Jonathan Frank, 6/22 Rye, NY |
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| 2021 (3.4) $\dfrac{2}{1\pmf} + 7 \times \sqrt{9}$ Jonathan Frank, 6/22 Rye, NY |
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| 2037 (2.0) $97 \times 21$ D.J. Demjanik, 8/13 Shawnee, KS |
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| 2042 (3.6) $\dfrac{2}{1\pmf} + 7 \times (\sqrt{9})!$ Jonathan Frank, 6/22 Rye, NY |
2048 (3.2) $2^{7 + 1 + \sqrt{9}}$ Jonathan Frank, 5/21 Rye, NY |
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| 2059 (2.0) $29 \times 71$ Kendra Stindt, 8/13 Topeka, KS |
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| 2063 (2.4) $\dfrac{2}{.1\%} + 7 \times 9$ Jonathan Frank, 6/22 Rye, NY |
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| 2079 (2.4) $\dfrac{2}{.1\%} + 79$ Jonathan Frank, 6/22 Rye, NY |
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| 2097 (2.4) $\dfrac{2}{.1\%} + 97$ Jonathan Frank, 6/22 Rye, NY |
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| 2186 (3.0) $\sqrt[2]{9^7} - 1$ Steve Wilson, 12/20 Lawrence, KS |
2187 (3.0) $\sqrt[2]{9^7} \times 1$ Steve Wilson, 9/20 Lawrence, KS |
2186 (3.0) $\sqrt[2]{9^7} + 1$ Steve Wilson, 12/20 Lawrence, KS |
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| 2399 (3.4) $\dfrac{72}{(\sqrt{9})\%} - 1$ Jonathan Frank, 6/22 Rye, NY |
2400 (3.4) $\dfrac{72}{(\sqrt{9})\%} \times 1$ Jonathan Frank, 6/22 Rye, NY |
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| 2401 (3.0) $7^{(9-1)/2}$ Gregory Bayer, 11/19 Sydney, NSW |
2403 (3.2) $7^{\sqrt{9} + 1} + 2$ Gregory Bayer, 11/20 Sydney, NSW |
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| 2430 (2.2) $\dfrac{9}{1\%} \times 2.7$ Jonathan Frank, 9/21 Rye, NY |
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| 2432 (3.0) $2^7 \times 19$ Hannah Maleki, 9/16 Overland Park, KS |
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| 2457 (2.0) $27 \times 91$ Echo Anderson, 12/13 Lenexa, KS |
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| 2511 (2.4) $\dfrac{279}{.\overline{1}}$ Jonathan Frank, 12/21 Rye, NY |
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| 2527 (3.0) $19^2 \times 7$ Justin Keck, 3/17 Lawrence, KS |
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| 2550 (3.4) $\dfrac{17}{2\%} \times \sqrt{9}$ Jonathan Frank, 6/22 Rye, NY |
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| 2592 (3.4) $\dfrac{9!}{7 \times 2} \times .1$ Parker Thomsen, 5/15 Lenexa, KS |
2600 (2.2) $\dfrac{91}{7\%} \times 2$ Jonathan Frank, 6/22 Rye, NY |
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| 2601 (3.0) $17^2 \times 9$ Sierra Henricks, 2/14 Olathe, KS |
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| 2673 (2.4) $\dfrac{297}{.\overline{1}}$ Jonathan Frank, 12/21 Rye, NY |
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| 2691 (2.2) $\dfrac{27}{1\%} - 9$ Jonathan Frank, 6/22 Rye, NY |
2694 (3.6) $\dfrac{27}{1\%} - (\sqrt{9})!$ Jonathan Frank, 6/22 Rye, NY |
2697 (3.4) $\dfrac{27}{1\%} - \sqrt{9}$ Jonathan Frank, 6/22 Rye, NY |
2700 (3.4) $\dfrac{9}{1\%} \times \sqrt{7 + 2}$ Jonathan Frank, 12/21 Rye, NY |
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| 2703 (3.4) $\dfrac{27}{1\%} + \sqrt{9}$ Jonathan Frank, 6/22 Rye, NY |
2706 (3.6) $\dfrac{27}{1\%} + (\sqrt{9})!$ Jonathan Frank, 6/22 Rye, NY |
2709 (2.2) $\dfrac{27}{1\%} + 9$ Jonathan Frank, 6/22 Rye, NY |
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| 2719 (2.0) $2719$ Sara Fridovich-Keil, 7/13 Decatur, GA |
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| 2790 (2.2) $\dfrac{279}{.1}$ Jonathan Frank, 6/22 Rye, NY |
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| 2791 (2.0) $2791$ Sara Fridovich-Keil, 7/13 Decatur, GA |
2800 (3.4) $\dfrac{7!}{9 \times .2 \times 1}$ Susan Vongphrachanh, 4/17 Kansas City, KS |
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| 2880 (3.2) $\dfrac{(9-1)!}{2 \times 7}$ Gregory Bayer, 11/19 Sydney, NSW |
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| 2893 (2.2) $\dfrac{29}{1\%} - 7$ Jonathan Frank, 6/22 Rye, NY |
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| 2907 (2.4) $\dfrac{29}{1\%} + 7$ Jonathan Frank, 6/22 Rye, NY |
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| 2917 (2.0) $2917$ Sara Fridovich-Keil, 7/13 Decatur, GA |
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| 2970 (2.2) $\dfrac{297}{.1}$ Jonathan Frank, 6/22 Rye, NY |
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| 2971 (2.0) $2971$ Sara Fridovich-Keil, 7/13 Decatur, GA |
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| 3031 (3.4) $7! - \dfrac{2}{1\pmf} - 9$ Jonathan Frank, 6/22 Rye, NY |
3034 (3.8) $7! - \dfrac{2}{1\pmf} - (\sqrt{9})!$ Jonathan Frank, 6/22 Rye, NY |
3037 (3.6) $7! - \dfrac{2}{1\pmf} - \sqrt{9}$ Jonathan Frank, 6/22 Rye, NY |
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| 3043 (3.6) $7! - \dfrac{2}{1\pmf} + \sqrt{9}$ Jonathan Frank, 6/22 Rye, NY |
3046 (3.8) $7! - \dfrac{2}{1\pmf} + (\sqrt{9})!$ Jonathan Frank, 6/22 Rye, NY |
3049 (3.4) $7! - \dfrac{2}{1\pmf} + 9$ Jonathan Frank, 6/22 Rye, NY |
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| 3087 (3.0) $7^{2+1} \times 9$ Gregory Bayer, 4/20 Sydney, NSW |
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| 3150 (3.2) $\dfrac{7}{1\%} \times \dfrac92$ Jonathan Frank, 7/21 Rye, NY |
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| 3185 (2.2) $91 \times \dfrac{7}{.2}$ Echo Anderson, 11/13 Lenexa, KS |
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| 3195 (2.2) $71 \times \dfrac{9}{.2}$ Echo Anderson, 11/13 Lenexa, KS |
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| 3240 (3.2) $(7 - 1)! \times \dfrac92$ Gregory Bayer, 5/20 Sydney, New South Wales |
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| 3241 (3.2) $91^2 - 7!$ Susan Vongphrachanh, 4/17 Kansas City, KS |
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| 3541 (2.2) $\dfrac{71}{2\%} - 9$ Jonathan Frank, 6/22 Rye, NY |
3544 (3.6) $\dfrac{71}{2\%} - (\sqrt{9})!$ Jonathan Frank, 6/22 Rye, NY |
3541 (3.4) $\dfrac{71}{2\%} - \sqrt{9}$ Jonathan Frank, 6/22 Rye, NY |
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| 3553 (3.4) $\dfrac{71}{2\%} + \sqrt{9}$ Jonathan Frank, 6/22 Rye, NY |
3556 (3.6) $\dfrac{71}{2\%} + (\sqrt{9})!$ Jonathan Frank, 6/22 Rye, NY |
3559 (2.2) $\dfrac{71}{2\%} + 9$ Jonathan Frank, 6/22 Rye, NY |
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| 3583 (3.0) $2^9 \times 7 - 1$ Sierra Henricks, 1/14 Olathe, KS |
3584 (3.0) $2^9 \times 7 \times 1$ D.J. Demjanik, 8/13 Shawnee, KS |
3585 (3.0) $2^9 \times 7 + 1$ Sierra Henricks, 4/14 Olathe, KS |
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| 3595 (2.2) $\dfrac{719}{.2}$ Jonathan Frank, 6/22 Rye, NY |
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| 3844 (3.0) $(7 \times 9 - 1)^2$ Steve Wilson, 9/20 Lawrence, KS |
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| 3949 (2.2) $\dfrac{79}{2\%} - 1$ David Anderson, 1/14 Olathe, KS |
3950 (2.2) $\dfrac{79}{2\%} \times 1$ David Anderson, 1/14 Olathe, KS |
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| 3951 (2.2) $\dfrac{79}{2\%} + 1$ Alyssa Trembly, 1/14 Spring Hill, KS |
3955 (2.2) $\dfrac{791}{.2}$ Jonathan Frank, 6/22 Rye, NY |
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| 3968 (3.0) $(9 \times 7)^2 - 1$ Huntly Cooper, 4/13 New York, NY |
3969 (3.0) $(9 \times 7)^2 \times 1$ Julia B., 7/13 Brooklyn, NY |
3970 (3.0) $(9 \times 7)^2 + 1$ Sierra Henricks, 3/14 Olathe, KS |
Page 1 (1-400), Page 2 (401-800), Page 3 (801-1200), Page 4 (1201-4000), Page 11 (4001+).