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The birthday of Integermania Master Jonathan Frank is November 4, 1990. Using one copy each of the numbers 4, 11, 19, and 90, and any standard operations, create each of the positive integers. All four numbers must be used, but no others. Also, the two-digit numbers 11, 19, and 90 may not be broken up. 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.
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| 418 (4.6) $11 \times 19 \times \sqrt{4} + \cos 90^\circ$ Jonathan Frank, 3/25 Rye, NY |
419 (4.6) $11 \times 19 \times \sqrt{4} + \sin 90^\circ$ Jonathan Frank, 3/25 Rye, NY |
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| 423 (1.0) $(90 + 11) \times 4 + 19$ Jonathan Frank, 1/23 Rye, NY |
425 (1.0) $(90 + 19) \times 4 - 11$ Jonathan Frank, 2/23 Rye, NY |
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| 440 (3.2) $19^{\sqrt{4}} - 11 + 90$ Jonathan Frank, 4/25 Rye, NY |
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| 447 (1.0) $(90 + 19) \times 4 + 11$ Jonathan Frank, 2/23 Rye, NY |
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| 462 (3.2) $19^{\sqrt{4}} + 11 + 90$ Jonathan Frank, 4/25 Rye, NY |
463 (4.6) $\dfrac{19}{4\%} - 11 - \sin 90^\circ$ Jonathan Frank, 4/25 Rye, NY |
464 (4.6) $\dfrac{19}{4\%} - 11 + \cos 90^\circ$ Jonathan Frank, 4/25 Rye, NY |
465 (4.6) $\dfrac{19}{4\%} - 11 + \sin 90^\circ$ Jonathan Frank, 4/25 Rye, NY |
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| 476 (1.0) $(19 \times 11 - 90) \times 4$ Jonathan Frank, 2/23 Rye, NY |
480 (1.0) $(90 + 19 + 11) \times 4$ Jonathan Frank, 2/23 Rye, NY |
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| 485 (4.6) $\dfrac{19}{4\%} + 11 - \sin 90^\circ$ Jonathan Frank, 5/25 Rye, NY |
486 (4.6) $\dfrac{19}{4\%} + 11 + \cos 90^\circ$ Jonathan Frank, 5/25 Rye, NY |
487 (4.6) $\dfrac{19}{4\%} + 11 + \sin 90^\circ$ Jonathan Frank, 5/25 Rye, NY |
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| 497 (1.0) $(11 - 4) \times (90 - 19)$ Jonathan Frank, 7/25 Rye, NY |
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| 505 (3.2) $(11 + 90) \times (4! - 19)$ Jonathan Frank, 11/25 Piscataway, NJ |
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| 520 (2.0) $411 + 19 + 90$ Jonathan Frank, 4/24 Rye, NY |
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| 554 (2.2) $\dfrac{19}{4\%} + 90 - 11$ Jonathan Frank, 2/23 Rye, NY |
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| 569 (1.0) $11 \times 19 + 90 \times 4$ Jonathan Frank, 2/24 Rye, NY |
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| 576 (2.2) $\dfrac{19}{4\%} + 90 + 11$ Jonathan Frank, 3/23 Rye, NY |
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| 630 (3.2) $(11 + 19) \times 4! - 90$ Jonathan Frank, 7/23 Rye, NY |
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| 660 (2.2) $\dfrac{19 + 11}{4\%} - 90$ Jonathan Frank, 3/23 Rye, NY |
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| 675 (1.0) $(19 + 11) \times \dfrac{90}{4}$ Jonathan Frank, 3/23 Rye, NY |
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| 688 (1.0) $(90 - 4) \times (19 - 11)$ Jonathan Frank, 3/23 Rye, NY |
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| 696 (3.2) $90 \times (19 - 11) - 4!$ Jonathan Frank, 3/23 Rye, NY |
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| 704 (3.2) $(90 - \sqrt{4}) \times (19 - 11)$ Jonathan Frank, 4/23 Rye, NY |
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| 716 (1.0) $90 \times (19 - 11) - 4$ Jonathan Frank, 4/23 Rye, NY |
718 (3.2) $90 \times (19 - 11) - \sqrt{4}$ Jonathan Frank, 4/23 Rye, NY |
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| 722 (3.2) $90 \times (19 - 11) + \sqrt{4}$ Jonathan Frank, 4/23 Rye, NY |
724 (1.0) $90 \times (19 - 11) + 4$ Jonathan Frank, 4/23 Rye, NY |
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| 736 (3.2) $(90 + \sqrt{4}) \times (19 - 11)$ Jonathan Frank, 5/23 Rye, NY |
737 (1.0) $(90 - 4 - 19) \times 11$ Jonathan Frank, 4/24 Rye, NY |
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| 744 (3.2) $90 \times (19 - 11) + 4!$ Jonathan Frank, 5/23 Rye, NY |
746 (1.0) $19 \times 11 \times 4 - 90$ Jonathan Frank, 5/23 Rye, NY |
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| 752 (1.0) $(90 + 4) \times (19 - 11)$ Jonathan Frank, 5/23 Rye, NY |
759 (3.2) $(90 - \sqrt{4} - 19) \times 11$ Jonathan Frank, 4/24 Rye, NY |
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| 763 (1.0) $(19 + 90) \times (11 - 4)$ Jonathan Frank, 11/25 Piscataway, NJ |
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| 777 (1.0) $(90 - 19) \times 11 - 4$ Jonathan Frank, 5/23 Rye, NY |
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| 785 (1.0) $(90 - 19) \times 11 + 4$ Jonathan Frank, 6/23 Rye, NY |
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| 803 (3.2) $(90 + \sqrt{4} - 19) \times 11$ Jonathan Frank, 4/24 Rye, NY |
810 (3.2) $(11 + 19) \times 4! + 90$ Jonathan Frank, 7/23 Rye, NY |
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| 825 (1.0) $(90 - 19 + 4) \times 11$ Jonathan Frank, 6/23 Rye, NY |
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| 836 (4.4) $11 \times 19 \times 4 + \cos 90^\circ$ Jonathan Frank, 3/25 Rye, NY |
837 (4.4) $11 \times 19 \times 4 + \sin 90^\circ$ Jonathan Frank, 3/25 Rye, NY |
840 (2.2) $\dfrac{19 + 11}{4\%} + 90$ Jonathan Frank, 6/23 Rye, NY |
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| 874 (1.0) $(90 - 11 \times 4) \times 19$ Jonathan Frank, 6/23 Rye, NY |
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| 912 (3.2) $(4! + 90) \times (19 - 11)$ Jonathan Frank, 11/25 Piscataway, NJ |
914 (1.0) $90 \times 11 - 19 \times 4$ Jonathan Frank, 6/23 Rye, NY |
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| 926 (1.0) $19 \times 11 \times 4 + 90$ Jonathan Frank, 7/23 Rye, NY |
927 (1.0) $(90 - 4) \times 11 - 19$ Jonathan Frank, 7/23 Rye, NY |
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| 935 (3.2) $(90 + 19 - 4!) \times 11$ Jonathan Frank, 7/25 Rye, NY |
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| 965 (1.0) $(90 - 4) \times 11 + 19$ Jonathan Frank, 7/23 Rye, NY |
967 (1.0) $90 \times 11 - 19 - 4$ Jonathan Frank, 8/23 Rye, NY |
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| 975 (1.0) $90 \times 11 - 19 + 4$ Jonathan Frank, 8/23 Rye, NY |
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| 1025 (2.0) $1119 - 90 - 4$ Jonathan Frank, 9/24 Rye, NY |
1027 (3.2) $1119 - 90 - \sqrt{4}$ Jonathan Frank, 9/24 Rye, NY |
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| 1031 (3.2) $1119 - 90 + \sqrt{4}$ Jonathan Frank, 9/24 Rye, NY |
1033 (2.0) $1119 - 90 + 4$ Jonathan Frank, 9/24 Rye, NY |
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| 1045 (3.2) $(90 - 19 + 4!) \times 11$ Jonathan Frank, 7/25 Rye, NY |
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| 1065 (1.0) $(4 + 11) \times (90 - 19)$ Jonathan Frank, 12/25 Piscataway, NJ |
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| 1075 (2.2) $\dfrac{90 - 4}{(19 - 11)\%}$ Jonathan Frank, 6/24 Rye, NY |
1080 (1.0) $(19 - 11 + 4) \times 90$ Jonathan Frank, 7/25 Rye, NY |
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| 1100 (3.4) $\dfrac{90 - \sqrt{4}}{(19 - 11)\%}$ Jonathan Frank, 6/24 Rye, NY |
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| 1150 (3.4) $\dfrac{90 + \sqrt{4}}{(19 - 11)\%}$ Jonathan Frank, 6/24 Rye, NY |
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| 1155 (1.0) $(90 - 4 + 19) \times 11$ Jonathan Frank, 5/24 Rye, NY |
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| 1167 (2.0) $1190 - 19 - 4$ Jonathan Frank, 9/24 Rye, NY |
1169 (3.2) $1190 - 19 - \sqrt{4}$ Jonathan Frank, 10/24 Rye, NY |
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| 1173 (3.2) $1190 - 19 + \sqrt{4}$ Jonathan Frank, 10/24 Rye, NY |
1175 (2.2) $\dfrac{90 + 4}{(19 - 11)\%}$ Jonathan Frank, 6/24 Rye, NY |
1177 (3.2) $(90 - \sqrt{4} + 19) \times 11$ Jonathan Frank, 5/24 Rye, NY |
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| 1185 (1.0) $(19 - 4) \times (90 - 11)$ Jonathan Frank, 9/25 Rye, NY |
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| 1205 (2.0) $1119 + 90 - 4$ Jonathan Frank, 10/24 Rye, NY |
1207 (3.2) $1119 + 90 - \sqrt{4}$ Jonathan Frank, 11/24 Rye, NY |
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| 1211 (3.2) $1119 + 90 + \sqrt{4}$ Jonathan Frank, 11/24 Rye, NY |
1213 (2.0) $1119 + 90 + 4$ Jonathan Frank, 10/24 Rye, NY |
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| 1221 (3.2) $(90 + \sqrt{4} + 19) \times 11$ Jonathan Frank, 5/24 Rye, NY |
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| 1243 (1.0) $(90 + 4 + 19) \times 11$ Jonathan Frank, 6/24 Rye, NY |
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| 1384 (2.0) $194 + 1190$ Jonathan Frank, 2/26 Piscataway, NJ |
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| 1417 (3.2) $(19 + 90) \times (4! - 11)$ Jonathan Frank, 12/25 Piscataway, NJ |
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| 1425 (1.0) $(90 - 4 - 11) \times 19$ Jonathan Frank, 11/24 Rye, NY |
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| 1446 (3.2) $90 \times 19 - 4! \times 11$ Jonathan Frank, 8/23 Rye, NY |
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| 1463 (3.2) $(90 - \sqrt{4} - 11) \times 19$ Jonathan Frank, 11/24 Rye, NY |
1465 (2.2) $\dfrac{19}{4\%} + 90 \times 11$ Jonathan Frank, 8/24 Rye, NY |
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| 1500 (2.2) $\dfrac{90 - 11 - 19}{4\%}$ Jonathan Frank, 7/24 Rye, NY |
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| 1515 (1.0) $(11 + 90) \times (19 - 4)$ Jonathan Frank, 12/25 Piscataway, NJ |
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| 1539 (3.2) $(90 + \sqrt{4} - 11) \times 19$ Jonathan Frank, 5/24 Rye, NY |
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| 1577 (1.0) $(90 + 4 - 11) \times 19$ Jonathan Frank, 5/24 Rye, NY |
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| 1609 (2.0) $419 + 1190$ Jonathan Frank, 2/26 Piscataway, NJ |
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| 1635 (1.0) $(4 + 11) \times (19 + 90)$ Jonathan Frank, 10/25 Piscataway, NJ |
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| 1666 (1.0) $90 \times 19 - 4 \times 11$ Jonathan Frank, 8/23 Rye, NY |
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| 1675 (3.2) $90 \times 19 - 4! - 11$ Jonathan Frank, 8/23 Rye, NY |
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| 1688 (3.2) $19 \times 90 - 11 \times \sqrt{4}$ Jonathan Frank, 9/23 Rye, NY |
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| 1695 (1.0) $19 \times 90 - 4 - 11$ Jonathan Frank, 9/23 Rye, NY |
1697 (3.2) $19 \times 90 - 4! + 11$ Jonathan Frank, 9/23 Rye, NY |
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| 1701 (3.2) $19 \times 90 - 11 + \sqrt{4}$ Jonathan Frank, 9/23 Rye, NY |
1703 (1.0) $19 \times 90 - 11 + 4$ Jonathan Frank, 9/23 Rye, NY |
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| 1717 (1.0) $19 \times 90 + 11 - 4$ Jonathan Frank, 10/23 Rye, NY |
1719 (3.2) $19 \times 90 + 11 - \sqrt{4}$ Jonathan Frank, 10/23 Rye, NY |
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| 1723 (3.2) $19 \times 90 + 4! - 11$ Jonathan Frank, 10/23 Rye, NY |
1725 (1.0) $19 \times 90 + 11 + 4$ Jonathan Frank, 10/23 Rye, NY |
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| 1732 (3.2) $19 \times 90 + 11 \times \sqrt{4}$ Jonathan Frank, 10/23 Rye, NY |
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| 1745 (3.2) $19 \times 90 + 4! + 11$ Jonathan Frank, 11/23 Rye, NY |
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| 1754 (1.0) $19 \times 90 + 4 \times 11$ Jonathan Frank, 11/23 Rye, NY |
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| 1817 (1.0) $(4 + 19) \times (90 - 11)$ Jonathan Frank, 11/25 Piscataway, NJ |
1819 (3.2) $1911 - 90 - \sqrt{4}$ Jonathan Frank, 12/24 Rye, NY |
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| 1823 (3.2) $1911 - 90 + \sqrt{4}$ Jonathan Frank, 12/24 Rye, NY |
1825 (2.0) $1911 - 90 + 4$ Jonathan Frank, 12/24 Rye, NY |
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| 1843 (1.0) $(90 - 4 + 11) \times 19$ Jonathan Frank, 3/24 Rye, NY |
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| 1881 (3.2) $(90 - \sqrt{4} + 11) \times 19$ Jonathan Frank, 3/24 Rye, NY |
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| 1957 (3.2) $(90 + \sqrt{4} + 11) \times 19$ Jonathan Frank, 3/24 Rye, NY |
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| 1968 (3.2) $(90 - 19 + 11) \times 4!$ Jonathan Frank, 7/25 Rye, NY |
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| 1974 (3.2) $19 \times 90 + 4! \times 11$ Jonathan Frank, 11/23 Rye, NY |
1975 (2.0) $1990 - 11 - 4$ Jonathan Frank, 12/24 Rye, NY |
1977 (3.2) $1990 - 11 - \sqrt{4}$ Jonathan Frank, 12/24 Rye, NY |
1980 (3.2) $(11 + 19) \times (90 - 4!)$ Jonathan Frank, 11/25 Piscataway, NJ |
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| 1981 (3.2) $1990 - 11 + \sqrt{4}$ Jonathan Frank, 1/25 Rye, NY |
1983 (2.0) $1990 - 11 + 4$ Jonathan Frank, 1/25 Rye, NY |
1985 (2.2) $\dfrac{11}{4\%} + 90 \times 19$ Jonathan Frank, 7/24 Rye, NY |
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| 1995 (1.0) $(90 + 4 + 11) \times 19$ Jonathan Frank, 3/24 Rye, NY |
1997 (2.0) $1911 + 90 - 4$ Jonathan Frank, 1/25 Rye, NY |
1999 (3.2) $1911 + 90 - \sqrt{4}$ Jonathan Frank, 1/25 Rye, NY |
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| 2003 (3.2) $1911 + 90 + \sqrt{4}$ Jonathan Frank, 1/25 Rye, NY |
2005 (2.0) $1911 + 90 + 4$ Jonathan Frank, 4/24 Rye, NY |
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| 2023 (2.0) $904 + 1119$ Jonathan Frank, 2/26 Piscataway, NJ |
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| 2050 (2.2) $\dfrac{90 + 11 - 19}{4\%}$ Jonathan Frank, 7/24 Rye, NY |
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| 2104 (2.0) $114 + 1990$ Jonathan Frank, 2/26 Piscataway, NJ |
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| 2130 (3.2) $90 \times 4! - 11 - 19$ Jonathan Frank, 8/25 Rye, NY |
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| 2152 (3.2) $90 \times 4! + 11 - 19$ Jonathan Frank, 8/25 Rye, NY |
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| 2168 (3.2) $90 \times 4! - 11 + 19$ Jonathan Frank, 8/25 Rye, NY |
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| 2190 (3.2) $90 \times 4! + 11 + 19$ Jonathan Frank, 8/25 Rye, NY |
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| 2250 (3.4) $\dfrac{90 \times \sqrt{4}}{(19 - 11)\%}$ Jonathan Frank, 11/23 Rye, NY |
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| 2323 (1.0) $(4 + 19) \times (11 + 90)$ Jonathan Frank, 10/25 Piscataway, NJ |
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| 2340 (1.0) $(19 + 11 - 4) \times 90$ Jonathan Frank, 8/25 Rye, NY |
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| 2352 (3.2) $(90 + 19 - 11) \times 4!$ Jonathan Frank, 10/25 Piscataway, NJ |
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| 2401 (2.0) $411 + 1990$ Jonathan Frank, 2/26 Piscataway, NJ |
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| 2450 (2.2) $\dfrac{90 - 11 + 19}{4\%}$ Jonathan Frank, 7/24 Rye, NY |
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| 2485 (3.2) $(4! + 11) \times (90 - 19)$ Jonathan Frank, 1/26 Piscataway, NJ |
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| 2580 (1.0) $(11 + 19) \times (90 - 4)$ Jonathan Frank, 1/26 Piscataway, NJ |
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| 2676 (3.2) $90 \times (19 + 11) - 4!$ Jonathan Frank, 11/23 Rye, NY |
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| 2696 (1.0) $90 \times (19 + 11) - 4$ Jonathan Frank, 12/23 Rye, NY |
2698 (3.2) $90 \times (19 + 11) - \sqrt{4}$ Jonathan Frank, 12/23 Rye, NY |
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| 2702 (3.2) $90 \times (19 + 11) + \sqrt{4}$ Jonathan Frank, 12/23 Rye, NY |
2704 (1.0) $90 \times (19 + 11) + 4$ Jonathan Frank, 12/23 Rye, NY |
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| 2724 (3.2) $90 \times (19 + 11) + 4!$ Jonathan Frank, 12/23 Rye, NY |
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| 2820 (1.0) $(11 + 19) \times (4 + 90)$ Jonathan Frank, 10/25 Piscataway, NJ |
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| 2880 (3.2) $(19 - 11 + 4!) \times 90$ Jonathan Frank, 10/25 Piscataway, NJ |
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| 3000 (2.2) $\dfrac{90 + 11 + 19}{4\%}$ Jonathan Frank, 7/24 Rye, NY |
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| 3060 (1.0) $(4 + 11 + 19) \times 90$ Jonathan Frank, 9/25 Rye, NY |
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| 3279 (3.2) $90 \times 4! + 1119$ Jonathan Frank, 5/25 Rye, NY |
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| 3397 (3.2) $(4! + 19) \times (90 - 11)$ Jonathan Frank, 1/26 Piscataway, NJ |
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| 3420 (3.2) $(11 + 19) \times (4! + 90)$ Jonathan Frank, 9/25 Rye, NY |
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| 3815 (3.2) $(4! + 11) \times (19 + 90)$ Jonathan Frank, 9/25 Rye, NY |
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| 3970 (4.6) $19^{\sqrt{4}} \times 11 - \sin 90^\circ$ Jonathan Frank, 11/25 Piscataway, NJ |
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| 3972 (4.6) $19^{\sqrt{4}} \times 11 + \sin 90^\circ$ Jonathan Frank, 11/25 Piscataway, NJ |
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| 4071 (3.2) $90 \times 4! + 1911$ Jonathan Frank, 5/25 Rye, NY |
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| 4343 (3.2) $(4! + 19) \times (11 + 90)$ Jonathan Frank, 9/25 Rye, NY |
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| 4500 (2.2) $90 \times \dfrac{4}{(19 - 11)\%}$ Jonathan Frank, 1/24 Rye, NY |
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| 7891 (3.2) $90^{\sqrt{4}} - 11 \times 19$ Jonathan Frank, 3/25 Rye, NY |
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| 8070 (3.2) $90^{\sqrt{4}} - 11 - 19$ Jonathan Frank, 8/24 Rye, NY |
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| 8092 (3.2) $90^{\sqrt{4}} + 11 - 19$ Jonathan Frank, 8/24 Rye, NY |
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| 8108 (3.2) $90^{\sqrt{4}} - 11 + 19$ Jonathan Frank, 8/24 Rye, NY |
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| 8130 (3.2) $90^{\sqrt{4}} + 11 + 19$ Jonathan Frank, 8/24 Rye, NY |
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| 8309 (3.2) $90^{\sqrt{4}} + 11 \times 19$ Jonathan Frank, 10/24 Rye, NY |
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| 12931 (3.0) $11^4 - 19 \times 90$ Jonathan Frank, 1/24 Rye, NY |
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| 14532 (3.0) $11^4 - 19 - 90$ Jonathan Frank, 2/24 Rye, NY |
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| 14570 (3.0) $11^4 + 19 - 90$ Jonathan Frank, 2/24 Rye, NY |
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| 14712 (3.0) $11^4 - 19 + 90$ Jonathan Frank, 2/24 Rye, NY |
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| 14750 (3.0) $11^4 + 19 + 90$ Jonathan Frank, 2/24 Rye, NY |
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| 16351 (3.0) $11^4 + 19 \times 90$ Jonathan Frank, 1/24 Rye, NY |
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| 17974 (1.0) $(90 - 4) \times 11 \times 19$ Jonathan Frank, 3/24 Rye, NY |
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| 18392 (3.2) $(90 - \sqrt{4}) \times 11 \times 19$ Jonathan Frank, 2/25 Rye, NY |
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| 18461 (3.4) $\dfrac{11!}{4! \times 90} - 19$ Jonathan Frank, 2/25 Rye, NY |
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| 18499 (3.4) $\dfrac{11!}{4! \times 90} + 19$ Jonathan Frank, 2/25 Rye, NY |
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| 19228 (3.2) $(90 + \sqrt{4}) \times 11 \times 19$ Jonathan Frank, 2/25 Rye, NY |
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| 19646 (1.0) $(90 + 4) \times 11 \times 19$ Jonathan Frank, 2/25 Rye, NY |
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| 27000 (3.4) $90 \times \dfrac{4!}{(19 - 11)\%}$ Jonathan Frank, 1/24 Rye, NY |
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| 75240 (1.0) $11 \times 4 \times 19 \times 90$ Jonathan Frank, 1/24 Rye, NY |
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