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Lawrence, Kansas, was settled in the year 1854. The original group of settlers, sponsored by the New England Emigrant Aid Company, are said to have eaten their first meal there on August 1 (which in shorthand would be 8/1/54). Using one copy each of the digits 1, 4, 5, and 8, 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.
PREVIOUS Page, Page 6 (2001+), ... Index to All Pages.
| 2002 (2.6) $\dfrac{8}{.4\%} + \dfrac{1}{.5}$ Steve Wilson, 6/26 Lawrence, KS |
2004 (2.4) $\dfrac{8}{.4\%} + 5 - 1$ Steve Wilson, 6/26 Lawrence, KS |
2005 (2.4) $\dfrac{8}{.4\%} + 5 \times 1$ Steve Wilson, 6/26 Lawrence, KS |
2006 (2.4) $\dfrac{8}{.4\%} + 5 + 1$ Steve Wilson, 6/26 Lawrence, KS |
2008 (2.2) $\dfrac{5 \times 4}{1\%} + 8$ Steve Wilson, 6/26 Lawrence, KS |
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| 2015 (2.4) $\dfrac{8}{.4\%} + 15$ Steve Wilson, 6/26 Lawrence, KS |
2020 (2.4) $\dfrac{81}{4\%} - 5$ Steve Wilson, 6/26 Lawrence, KS |
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| 2025 (2.6) $\dfrac{1.8 \times 5}{.\overline{4}\%}$ Steve Wilson, 6/26 Lawrence, KS |
2030 (2.4) $\dfrac{81}{4\%} + 5$ Steve Wilson, 6/26 Lawrence, KS |
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| 2050 (2.4) $\dfrac{\dfrac{8}{4\%} + 5}{.1}$ Steve Wilson, 6/26 Lawrence, KS |
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| 2051 (2.4) $\dfrac{8}{.4\%} + 51$ Steve Wilson, 6/26 Lawrence, KS |
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| 2072 (2.0) $4 \times 518$ Steve Wilson, 6/26 Lawrence, KS |
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| 2088 (2.4) $\dfrac{58 \times 4}{.\overline{1}}$ Steve Wilson, 6/26 Lawrence, KS |
2090 (2.0) $5 \times 418$ Steve Wilson, 6/26 Lawrence, KS |
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| 2100 (2.2) $\dfrac{85 - 1}{4\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 2124 (2.2) $\dfrac{85}{4\%} - 1$ Steve Wilson, 6/26 Lawrence, KS |
2125 (2.2) $\dfrac{85}{4\%} \times 1$ Steve Wilson, 6/26 Lawrence, KS |
2126 (2.2) $\dfrac{85}{4\%} + 1$ Steve Wilson, 6/26 Lawrence, KS |
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| 2150 (2.2) $\dfrac{81 + 5}{4\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 2160 (2.4) $\dfrac{48 \times 5}{.\overline{1}}$ Steve Wilson, 6/26 Lawrence, KS |
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| 2240 (2.2) $\dfrac{14 \times 8}{5\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 2250 (2.2) $\dfrac{18 \times 5}{4\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 2320 (2.2) $\dfrac{58 \times 4}{.1}$ Steve Wilson, 6/26 Lawrence, KS |
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| 2324 (2.0) $4 \times 581$ Steve Wilson, 6/26 Lawrence, KS |
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| 2378 (2.0) $41 \times 58$ Jonathan Frank, 5/24 Rye, NY |
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| 2400 (2.2) $\dfrac{48 \times 5}{.1}$ Steve Wilson, 6/26 Lawrence, KS |
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| 2405 (2.0) $5 \times 481$ Steve Wilson, 6/26 Lawrence, KS |
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| 2448 (2.0) $48 \times 51$ Jonathan Frank, 5/24 Rye, NY |
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| 2550 (2.2) $\dfrac{51 \times 4}{8\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 2700 (2.6) $\dfrac{1.5 \times 8}{.\overline{4}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 2799 (3.4) $4! \times 5! - 81$ Jonathan Frank, 11/24 Rye, NY |
2800 (2.4) $\dfrac{18 - 4}{.5\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 2862 (3.4) $4! \times 5! - 18$ Jonathan Frank, 11/24 Rye, NY |
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| 2871 (3.4) $4! \times 5! - 8 - 1$ Jonathan Frank, 11/24 Rye, NY |
2872 (3.4) $4! \times 5! - 8 \times 1$ Jonathan Frank, 12/24 Rye, NY |
2873 (3.4) $4! \times 5! - 8 + 1$ Jonathan Frank, 12/24 Rye, NY |
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| 2887 (3.4) $4! \times 5! + 8 - 1$ Jonathan Frank, 12/24 Rye, NY |
2888 (3.4) $4! \times 5! + 8 \times 1$ Jonathan Frank, 12/24 Rye, NY |
2889 (3.4) $4! \times 5! + 8 + 1$ Jonathan Frank, 12/24 Rye, NY |
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| 2898 (3.4) $4! \times 5! + 18$ Jonathan Frank, 1/25 Rye, NY |
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| 2925 (2.6) $\dfrac{18 - 5}{.\overline{4}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 2960 (2.2) $\dfrac{148}{5\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 2961 (3.4) $4! \times 5! + 18$ Jonathan Frank, 1/25 Rye, NY |
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| 3000 (2.2) $\dfrac{15 \times 8}{4\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 3060 (2.4) $\dfrac{85 \times 4}{.\overline{1}}$ Steve Wilson, 6/26 Lawrence, KS |
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| 3240 (2.4) $\dfrac{45 \times 8}{.\overline{1}}$ Steve Wilson, 6/26 Lawrence, KS |
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| 3250 (2.4) $\dfrac{18 - 5}{.4\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 3260 (2.0) $4 \times 815$ Steve Wilson, 6/26 Lawrence, KS |
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| 3320 (2.0) $8 \times 415$ Steve Wilson, 6/26 Lawrence, KS |
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| 3330 (2.8) $\dfrac{4.5 - .8}{.\overline{1}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 3400 (2.2) $\dfrac{85 \times 4}{.1}$ Steve Wilson, 6/26 Lawrence, KS |
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| 3404 (2.0) $4 \times 851$ Steve Wilson, 6/26 Lawrence, KS |
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| 3485 (2.0) $41 \times 85$ Carter Miller, 5/22 Lawrence, KS |
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| 3600 (2.2) $\dfrac{45 \times 8}{.1}$ Steve Wilson, 6/26 Lawrence, KS |
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| 3608 (2.0) $8 \times 451$ Steve Wilson, 6/26 Lawrence, KS |
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| 3645 (2.0) $45 \times 81$ Jonathan Frank, 5/24 Rye, NY |
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| 3680 (2.2) $\dfrac{184}{5\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 3700 (2.2) $\dfrac{45 - 8}{1\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 3780 (2.4) $\dfrac{84 \times 5}{.\overline{1}}$ Steve Wilson, 6/26 Lawrence, KS |
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| 3870 (2.8) $\dfrac{4.8 - .5}{.\overline{1}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 3888 (2.4) $\dfrac{54 \times 8}{.\overline{1}}$ Steve Wilson, 6/26 Lawrence, KS |
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| 3950 (2.2) $\dfrac{158}{4\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 3975 (3.2) $8^4 - 5! - 1$ Jonathan Frank, 9/24 Rye, NY |
3976 (3.2) $8^4 - 5! \times 1$ Jonathan Frank, 9/24 Rye, NY |
3977 (3.2) $8^4 - 5! + 1$ Jonathan Frank, 9/24 Rye, NY |
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| 4045 (3.0) $8^4 - 51$ Satchel Koch, 11/21 Lawrence, KS |
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| 4070 (2.0) $5 \times 814$ Steve Wilson, 6/26 Lawrence, KS |
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| 4081 (3.0) $8^4 - 15$ Jonathan Frank, 1/25 Rye, NY |
4090 (3.0) $8^4 - 5 - 1$ Jonathan Frank, 9/24 Rye, NY |
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| 4091 (3.0) $8^4 - 5 \times 1$ Jonathan Frank, 9/24 Rye, NY |
4092 (3.0) $8^4 - 5 + 1$ Jonathan Frank, 10/24 Rye, NY |
4100 (3.0) $8^4 + 5 - 1$ Jonathan Frank, 10/24 Rye, NY |
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| 4101 (3.0) $8^4 + 5 \times 1$ Jonathan Frank, 10/24 Rye, NY |
4102 (3.0) $8^4 + 5 + 1$ Jonathan Frank, 10/24 Rye, NY |
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| 4111 (3.0) $8^4 + 15$ Maddy Malm, 2/22 Lawrence, KS |
4112 (2.0) $8 \times 514$ Steve Wilson, 6/26 Lawrence, KS |
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| 4122 (2.4) $\dfrac{458}{.\overline{1}}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4140 (2.8) $\dfrac{5.4 - .8}{.\overline{1}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4147 (3.0) $8^4 + 51$ Satchel Koch, 11/21 Lawrence, KS |
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| 4158 (2.0) $4158$ Jonathan Frank, 3/24 Rye, NY |
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| 4185 (2.0) $4185$ Jonathan Frank, 3/24 Rye, NY |
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| 4200 (2.2) $\dfrac{84 \times 5}{.1}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4205 (2.0) $5 \times 841$ Steve Wilson, 6/26 Lawrence, KS |
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| 4215 (3.2) $8^4 + 5! - 1$ Jonathan Frank, 10/24 Rye, NY |
4216 (3.2) $8^4 + 5! \times 1$ Jonathan Frank, 11/24 Rye, NY |
4217 (3.2) $8^4 + 5! + 1$ Jonathan Frank, 11/24 Rye, NY |
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| 4284 (2.0) $51 \times 84$ Jonathan Frank, 5/24 Rye, NY |
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| 4300 (2.2) $\dfrac{48 - 5}{1\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4320 (2.2) $\dfrac{54 \times 8}{.1}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4328 (2.0) $541 \times 8$ Carter Miller, 5/22 Lawrence, KS |
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| 4365 (2.4) $\dfrac{485}{.\overline{1}}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4374 (2.0) $54 \times 81$ Jonathan Frank, 5/24 Rye, NY |
4375 (3.0) $5^4 \times (8 - 1)$ Jonathan Frank, 1/25 Rye, NY |
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| 4400 (2.4) $\dfrac{14 + 8}{.5\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4500 (2.4) $\dfrac{41 - 5}{.8\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4518 (2.0) $4518$ Jonathan Frank, 3/24 Rye, NY |
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| 4580 (2.2) $\dfrac{458}{.1}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4581 (2.0) $4581$ Jonathan Frank, 6/24 Rye, NY |
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| 4600 (2.2) $\dfrac{54 - 8}{1\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4625 (2.2) $\dfrac{185}{4\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4770 (2.8) $\dfrac{4.5 + .8}{.\overline{1}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4815 (2.0) $4815$ Jonathan Frank, 6/24 Rye, NY |
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| 4850 (2.2) $\dfrac{485}{.1}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4851 (2.0) $4851$ Jonathan Frank, 6/24 Rye, NY |
4860 (2.8) $\dfrac{5.8 - .4}{.\overline{1}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4932 (2.4) $\dfrac{548}{.\overline{1}}$ Steve Wilson, 6/26 Lawrence, KS |
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| 5000 (3.0) $5^4 \times 8 \times 1$ Jonathan Frank, 11/23 Rye, NY |
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| 5148 (2.0) $5148$ Steve Wilson, 6/26 Lawrence, KS |
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| 5175 (2.6) $\dfrac{15 + 8}{.\overline{4}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 5184 (2.0) $5184$ Steve Wilson, 6/26 Lawrence, KS |
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| 5256 (2.4) $\dfrac{584}{.\overline{1}}$ Steve Wilson, 6/26 Lawrence, KS |
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| 5300 (2.2) $\dfrac{45 + 8}{1\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 5400 (2.2) $\dfrac{58 - 4}{1\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 5418 (2.0) $5418$ Steve Wilson, 6/26 Lawrence, KS |
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| 5480 (2.2) $\dfrac{548}{.1}$ Steve Wilson, 6/26 Lawrence, KS |
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| 5481 (2.0) $5481$ Steve Wilson, 6/26 Lawrence, KS |
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| 5500 (2.4) $\dfrac{45 - 1}{.8\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 5580 (2.8) $\dfrac{5.4 + .8}{.\overline{1}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 5625 (3.0) $5^4 \times (8 + 1)$ Jonathan Frank, 1/25 Rye, NY |
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| 5750 (2.4) $\dfrac{15 + 8}{.4\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 5814 (2.0) $5814$ Steve Wilson, 6/26 Lawrence, KS |
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| 5840 (2.2) $\dfrac{584}{.1}$ Steve Wilson, 6/26 Lawrence, KS |
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| 5841 (2.0) $5841$ Steve Wilson, 6/26 Lawrence, KS |
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| 6200 (2.2) $\dfrac{54 + 8}{1\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 6425 (2.2) $\dfrac{514}{8\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 6480 (2.2) $\dfrac{81 \times 4}{5\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 6560 (2.2) $\dfrac{41 \times 8}{5\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 6600 (2.4) $\dfrac{41 - 8}{.5\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 6749 (2.4) $\dfrac{54}{.8\%} - 1$ Steve Wilson, 6/26 Lawrence, KS |
6750 (2.4) $\dfrac{54}{.8\%} \times 1$ Steve Wilson, 6/26 Lawrence, KS |
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| 6751 (2.4) $\dfrac{54}{.8\%} + 1$ Steve Wilson, 6/26 Lawrence, KS |
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| 7110 (2.8) $\dfrac{8.4 - .5}{.\overline{1}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 7290 (2.8) $\dfrac{8.5 - .4}{.\overline{1}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 7500 (2.4) $\dfrac{15 \times 4}{.8\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 7605 (2.4) $\dfrac{845}{.\overline{1}}$ Steve Wilson, 6/26 Lawrence, KS |
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| 7686 (2.4) $\dfrac{854}{.\overline{1}}$ Steve Wilson, 6/26 Lawrence, KS |
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| 7900 (2.2) $\dfrac{84 - 5}{1\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 8010 (2.8) $\dfrac{8.4 + .5}{.\overline{1}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 8100 (2.2) $\dfrac{85 - 4}{1\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 8145 (2.0) $8145$ Jonathan Frank, 7/24 Rye, NY |
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| 8154 (2.0) $8154$ Jonathan Frank, 7/24 Rye, NY |
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| 8360 (2.2) $\dfrac{418}{5\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 8415 (2.0) $8415$ Jonathan Frank, 7/24 Rye, NY |
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| 8450 (2.2) $\dfrac{845}{.1}$ Steve Wilson, 6/26 Lawrence, KS |
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| 8451 (2.0) $8451$ Jonathan Frank, 8/24 Rye, NY |
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| 8514 (2.0) $8514$ Jonathan Frank, 8/24 Rye, NY |
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| 8540 (2.2) $\dfrac{854}{.1}$ Steve Wilson, 6/26 Lawrence, KS |
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| 8541 (2.0) $8541$ Jonathan Frank, 8/24 Rye, NY |
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| 8750 (2.4) $\dfrac{14 \times 5}{.8\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 8900 (2.2) $\dfrac{84 + 5}{1\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 9180 (2.6) $\dfrac{5.1 \times 8}{.\overline{4}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 9400 (2.4) $\dfrac{48 - 1}{.5\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 9599 (2.4) $\dfrac{48}{.5\%} - 1$ Steve Wilson, 6/26 Lawrence, KS |
9600 (2.4) $\dfrac{48}{.5\%} \times 1$ Steve Wilson, 6/26 Lawrence, KS |
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| 9601 (2.4) $\dfrac{48}{.5\%} + 1$ Steve Wilson, 6/26 Lawrence, KS |
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| 9620 (2.2) $\dfrac{481}{5\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 9675 (2.6) $\dfrac{51 - 8}{.\overline{4}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 9800 (2.4) $\dfrac{41 + 8}{.5\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 11250 (3.0) $5^4 \times 18$ Jonathan Frank, 8/24 Rye, NY |
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| 32727 (3.0) $8^5 - 41$ Maddy Malm, 2/22 Lawrence, KS |
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| 32754 (3.0) $8^5 - 14$ J.P. Gitau, 12/21 Lawrence, KS |
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| 32771 (3.2) $1 + 8^5 + \sqrt{4}$ J.P. Gitau, 2/22 Lawrence, KS |
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| 32782 (3.0) $8^5 + 14$ Maddy Malm, 2/22 Lawrence, KS |
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| 32809 (3.0) $8^5 + 41$ Maddy Malm, 2/22 Lawrence, KS |
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| 50625 (3.0) $5^4 \times 81$ Jonathan Frank, 8/24 Rye, NY |
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| 390611 (3.0) $5^8 - 14$ J.P. Gitau, 12/21 Lawrence, KS |
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| 16777216 (3.0) $8^{5 - 1 + 4}$ Maddy Malm, 2/22 Lawrence, KS |
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| 268435456 (3.0) $4^{5+8+1}$ Carter Miller, 9/21 Lawrence, KS |
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| 1073741824 (3.0) $8^{5+1+4}$ Carter Miller, 9/21 Lawrence, KS |
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| 1220703125 (3.0) $5^{1+4+8}$ Carter Miller, 3/22 Lawrence, KS |
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| 113947428721 (3.0) $581^4$ Carter Miller, 5/22 Lawrence, KS |
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| 524467088401 (3.0) $851^4$ Carter Miller, 3/22 Lawrence, KS |
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| 25746925826401 (3.0) $481^5$ Carter Miller, 5/22 Lawrence, KS |
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