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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 12 (4401+), ... Index to All Pages.
| 4416 (2.6) $\dfrac{5}{.\overline{1}\%} - 84$ Steve Wilson, 6/26 Lawrence, KS |
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| 4449 (3.0) $\dfrac{.4}{.\overline{8}\%\%} - 51$ Steve Wilson, 6/26 Lawrence, KS |
4450 (2.8) $\dfrac{5}{.\overline{1}\%} - \dfrac{4}{8\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4452 (2.6) $\dfrac{5}{.\overline{1}\%} - 48$ Steve Wilson, 6/26 Lawrence, KS |
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| 4468 (2.6) $\dfrac{5}{.\overline{1}\%} - 8 \times 4$ Steve Wilson, 6/26 Lawrence, KS |
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| 4480 (2.6) $\dfrac{5}{.\overline{1}\%} - \dfrac{8}{.4}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4485 (3.0) $\dfrac{.4}{.\overline{8}\%\%} - 15$ Steve Wilson, 6/26 Lawrence, KS |
4488 (2.6) $\dfrac{5}{.\overline{1}\%} - 8 - 4$ Steve Wilson, 6/26 Lawrence, KS |
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| 4494 (3.0) $\dfrac{.4}{.\overline{8}\%\%} - 5 - 1$ Steve Wilson, 6/26 Lawrence, KS |
4495 (2.8) $\dfrac{5}{.\overline{1}\%} - \dfrac{4}{.8}$ Steve Wilson, 6/26 Lawrence, KS |
4496 (2.6) $\dfrac{5}{.\overline{1}\%} - 8 + 4$ Steve Wilson, 6/26 Lawrence, KS |
4498 (2.6) $\dfrac{5}{.\overline{1}\%} - \dfrac84$ Steve Wilson, 6/26 Lawrence, KS |
4500 (2.4) $\dfrac{41 - 5}{.8\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4502 (2.6) $\dfrac{5}{.\overline{1}\%} + \dfrac84$ Steve Wilson, 6/26 Lawrence, KS |
4504 (2.6) $\dfrac{5}{.\overline{1}\%} + 8 - 4$ Steve Wilson, 6/26 Lawrence, KS |
4505 (2.8) $\dfrac{5}{.\overline{1}\%} + \dfrac{4}{.8}$ Steve Wilson, 6/26 Lawrence, KS |
4506 (3.0) $\dfrac{.4}{.\overline{8}\%\%} + 5 + 1$ Steve Wilson, 6/26 Lawrence, KS |
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| 4512 (2.6) $\dfrac{5}{.\overline{1}\%} + 8 + 4$ Steve Wilson, 6/26 Lawrence, KS |
4515 (3.0) $\dfrac{.4}{.\overline{8}\%\%} + 15$ Steve Wilson, 6/26 Lawrence, KS |
4518 (2.0) $4518$ Jonathan Frank, 3/24 Rye, NY |
4520 (2.8) $\dfrac{5}{.\overline{1}\%} + \dfrac{8}{.4}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4532 (2.6) $\dfrac{5}{.\overline{1}\%} + 8 \times 4$ Steve Wilson, 6/26 Lawrence, KS |
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| 4548 (2.6) $\dfrac{5}{.\overline{1}\%} + 48$ Steve Wilson, 6/26 Lawrence, KS |
4550 (2.8) $\dfrac{5}{.\overline{1}\%} + \dfrac{4}{8\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 4551 (3.0) $\dfrac{.4}{.\overline{8}\%\%} + 51$ Steve Wilson, 6/26 Lawrence, KS |
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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 |
4584 (2.6) $\dfrac{5}{.\overline{1}\%} + 84$ Steve Wilson, 6/26 Lawrence, KS |
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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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| 4700 (2.8) $\dfrac{5}{.\overline{1}\%} + \dfrac{8}{4\%}$ 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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| 4837 (3.6) $8! \times 5!\pm - 1.4$ Steve Wilson, 7/26 Lawrence, KS |
4838 (3.8) $8! \times 5!\pm - 1 \times .4$ Steve Wilson, 7/26 Lawrence, KS |
4839 (3.8) $8! \times 5!\pm + 1 - .4$ Steve Wilson, 7/26 Lawrence, KS |
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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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| 4950 (2.6) $\dfrac{45 - 1}{.\overline{8}\%}$ 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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| 5584 (3.0) $\dfrac{.5}{.\overline{8}\%\%} - 41$ Steve Wilson, 6/26 Lawrence, KS |
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| 5611 (3.0) $\dfrac{.5}{.\overline{8}\%\%} - 14$ Steve Wilson, 6/26 Lawrence, KS |
5620 (3.0) $\dfrac{.5}{.\overline{8}\%\%} - 4 - 1$ Steve Wilson, 6/26 Lawrence, KS |
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| 5621 (3.0) $\dfrac{.5}{.\overline{8}\%\%} - 4 \times 1$ Steve Wilson, 6/26 Lawrence, KS |
5622 (3.0) $\dfrac{.5}{.\overline{8}\%\%} - 4 + 1$ Steve Wilson, 6/26 Lawrence, KS |
5625 (3.0) $5^4 \times (8 + 1)$ Jonathan Frank, 1/25 Rye, NY |
5628 (3.0) $\dfrac{.5}{.\overline{8}\%\%} + 4 - 1$ Steve Wilson, 6/26 Lawrence, KS |
5629 (3.0) $\dfrac{.5}{.\overline{8}\%\%} + 4 \times 1$ Steve Wilson, 6/26 Lawrence, KS |
5630 (3.0) $\dfrac{.5}{.\overline{8}\%\%} + 4 + 1$ Steve Wilson, 6/26 Lawrence, KS |
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| 5639 (3.0) $\dfrac{.5}{.\overline{8}\%\%} + 14$ Steve Wilson, 6/26 Lawrence, KS |
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| 5666 (3.0) $\dfrac{.5}{.\overline{8}\%\%} + 41$ Steve Wilson, 6/26 Lawrence, KS |
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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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| 5832 (2.6) $\dfrac{8.1 \times 4}{.\overline{5}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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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| 5904 (2.6) $\dfrac{4.1 \times 8}{.\overline{5}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 5940 (2.6) $\dfrac{41 - 8}{.\overline{5}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 6074 (2.6) $\dfrac{54}{.\overline{8}\%} - 1$ Steve Wilson, 6/26 Lawrence, KS |
6075 (2.6) $\dfrac{54}{.\overline{8}\%} \times 1$ Steve Wilson, 6/26 Lawrence, KS |
6076 (2.6) $\dfrac{54}{.\overline{8}\%} + 1$ Steve Wilson, 6/26 Lawrence, KS |
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| 6144 (3.0) $8^4 \times 1.5$ Steve Wilson, 7/26 Lawrence, KS |
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| 6200 (2.2) $\dfrac{54 + 8}{1\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 6400 (3.0) $\dfrac{8}{.\overline{1}\%} - \dfrac{4}{.5\%}$ 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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| 6525 (3.2) $\dfrac{.8 - .51}{.\overline{4}\%\%}$ 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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| 6840 (3.2) $\dfrac{.48 - .1}{.\overline{5}\%\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 6975 (3.2) $\dfrac{.81 - .5}{.\overline{4}\%\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 7020 (3.2) $\dfrac{.8 - .41}{.\overline{5}\%\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 7075 (2.8) $\dfrac{8}{.\overline{1}\%} - \dfrac{5}{4\%}$ 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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| 7120 (2.8) $\dfrac{8}{.\overline{1}\%} - \dfrac{4}{5\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 7146 (2.6) $\dfrac{8}{.\overline{1}\%} - 54$ Steve Wilson, 6/26 Lawrence, KS |
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| 7155 (2.6) $\dfrac{8}{.\overline{1}\%} - 45$ Steve Wilson, 6/26 Lawrence, KS |
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| 7180 (2.6) $\dfrac{8}{.\overline{1}\%} - 5 \times 4$ Steve Wilson, 6/26 Lawrence, KS |
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| 7191 (2.6) $\dfrac{8}{.\overline{1}\%} - 5 - 4$ Steve Wilson, 6/26 Lawrence, KS |
7192 (2.8) $\dfrac{8}{.\overline{1}\%} - \dfrac{4}{.5}$ Steve Wilson, 6/26 Lawrence, KS |
7193 (3.0) $\dfrac{.4}{.\overline{5}\%\%} - 8 + 1$ Steve Wilson, 6/26 Lawrence, KS |
7199 (2.6) $\dfrac{8}{.\overline{1}\%} - 5 + 4$ Steve Wilson, 6/26 Lawrence, KS |
7200 (2.6) $\dfrac{8}{.\overline{1}\%} \times (5 - 4)$ Steve Wilson, 6/26 Lawrence, KS |
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| 7201 (2.6) $\dfrac{8}{.\overline{1}\%} + 5 - 4$ Steve Wilson, 6/26 Lawrence, KS |
7207 (3.0) $\dfrac{.4}{.\overline{5}\%\%} + 8 - 1$ Steve Wilson, 6/26 Lawrence, KS |
7208 (2.8) $\dfrac{8}{.\overline{1}\%} + \dfrac{4}{.5}$ Steve Wilson, 6/26 Lawrence, KS |
7209 (2.6) $\dfrac{8}{.\overline{1}\%} + 5 + 4$ Steve Wilson, 6/26 Lawrence, KS |
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| 7220 (2.6) $\dfrac{8}{.\overline{1}\%} + 5 \times 4$ Steve Wilson, 6/26 Lawrence, KS |
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| 7236 (2.8) $\dfrac{41 - .8}{.\overline{5}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 7245 (2.6) $\dfrac{8}{.\overline{1}\%} + 45$ Steve Wilson, 6/26 Lawrence, KS |
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| 7254 (2.6) $\dfrac{8}{.\overline{1}\%} + 54$ Steve Wilson, 6/26 Lawrence, KS |
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| 7280 (2.8) $\dfrac{8}{.\overline{1}\%} + \dfrac{4}{5\%}$ 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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| 7325 (2.8) $\dfrac{8}{.\overline{1}\%} + \dfrac{5}{4\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 7380 (3.2) $\dfrac{.81 - .4}{.\overline{5}\%\%}$ 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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| 7875 (2.6) $\dfrac{14 \times 5}{.\overline{8}\%}$ 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 |
8460 (2.6) $\dfrac{48 - 1}{.\overline{5}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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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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| 8622 (2.8) $\dfrac{48 - .1}{.\overline{5}\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 8639 (2.6) $\dfrac{48}{.\overline{5}\%} - 1$ Steve Wilson, 6/26 Lawrence, KS |
8640 (2.6) $\dfrac{48}{.\overline{5}\%} \times 1$ Steve Wilson, 6/26 Lawrence, KS |
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| 8641 (2.6) $\dfrac{48}{.\overline{5}\%} + 1$ Steve Wilson, 6/26 Lawrence, KS |
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| 8750 (2.4) $\dfrac{14 \times 5}{.8\%}$ Steve Wilson, 6/26 Lawrence, KS |
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| 8820 (2.6) $\dfrac{41 + 8}{.\overline{5}\%}$ 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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| 32767 (3.4) $8^5 - (\sqrt{4})! + 1$ Rayhan Ahmed, 6/26 Dhaka, Bangladesh |
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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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