$\def\pm{{ ‰}} \def\pmf{{ ‰ \phantom.}} \def\pmm{{ ‰ \! ‰}} \def\pmmf{{ ‰ \! ‰ \phantom\%}}$

## Integermania!

#### Lawrence

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! Five "new" or "improved" solutions per person per month are accepted.

Page 1 (1-400).

 1 (1.0) $\dfrac{1 + 8}{5 + 4}$ Steve Wilson, 9/20Lawrence, KS 2 (1.0) $\dfrac{8 + 4}{5 + 1}$ Steve Wilson, 12/20Lawrence, KS 3 (1.0) $\dfrac{8 + 4}{5 - 1}$ Jacob Heasley, 4/21Grove City, PA 4 (1.0) $\dfrac{8}{5 - 4 + 1}$ Jonathan Frank, 4/21Rye, NY 5 (1.0) $\left( \dfrac84 - 1 \right) \times 5$ Jonathan Frank, 4/21Rye, NY 6 (1.0) $4 + 8 - (5 + 1)$ Elizabeth Rozzi, 12/20Lawrence, KS 7 (1.0) $8 \times 1 - 5 + 4$ Elizabeth Rozzi, 12/20Lawrence, KS 8 (1.0) $8 + 5 - 4 - 1$ Jonathan Frank, 4/21Rye, NY 9 (1.0) $8 + 5 - 4 \times 1$ Jacob Heasley, 4/21Grove City, PA 10 (1.0) $1 + 8 + 5 - 4$ Jacob Heasley, 4/21Grove City, PA 11 (1.0) $5 \times 4 - 8 - 1$ Dana Reigle, 4/21Grove City, PA 12 (1.0) $5 \times 4 \times 1 - 8$ Dana Reigle, 4/21Grove City, PA 13 (1.0) $4 \times 5 - 8 + 1$ Elizabeth Rozzi, 12/20Lawrence, KS 14 (2.2) $8 + 4 + \dfrac{1}{.5}$ Steve Wilson, 4/21Lawrence, KS 15 (1.0) $(8 - 4 - 1) \times 5$ Steve Wilson, 4/21Lawrence, KS 16 (1.0) $8 + 5 + 4 - 1$ Steve Wilson, 4/21Lawrence, KS 17 (1.0) $8 \times 1 + 5 + 4$ Elizabeth Rozzi, 12/20Lawrence, KS 18 (1.0) $1 + 8 + 5 + 4$ Jacob Heasley, 4/21Grove City, PA 19 (1.0) $(8 - 4) \times 5 - 1$ Steve Wilson, 4/21Lawrence, KS 20 (1.0) $(8 - 4) \times 5 \times 1$ Steve Wilson, 4/21Lawrence, KS 21 (1.0) $(8 - 4) \times 5 + 1$ Jonathan Frank, 5/21Rye, NY 22 (2.2) $\dfrac{8 + 4 - 1}{.5}$ Jonathan Frank, 6/21Rye, NY 23 (1.0) $(8 - 1) \times 4 - 5$ Jonathan Frank, 5/21Rye, NY 24 (1.0) $(8 - 4) \times (5 + 1)$ Jonathan Frank, 4/21Rye, NY 25 (1.0) $(8 - 4 + 1) \times 5$ Jonathan Frank, 4/21Rye, NY 26 (1.0) $8 \times 4 - 5 - 1$ Jonathan Frank, 5/21Rye, NY 27 (1.0) $5 \times 4 + 8 - 1$ Jonathan Frank, 5/21Rye, NY 28 (1.0) $5 \times 4 + 8 \times 1$ Jonathan Frank, 6/21Rye, NY 29 (1.0) $5 \times 4 + 8 + 1$ Jonathan Frank, 6/21Rye, NY 30 (2.0) $15 \times \dfrac84$ Steve Wilson, 6/21Lawrence, KS 31 (1.0) $4 \times (8 + 1) - 5$ Elizabeth Rozzi, 12/20Lawrence, KS 32 (1.0) $4 \times (5 + 1) + 8$ Steve Wilson, 6/21Lawrence, KS 33 (1.0) $(8 - 1) \times 4 + 5$ Jonathan Frank, 6/21Rye, NY 34 (2.2) $84 - \dfrac{5}{.1}$ Steve Wilson, 7/21Lawrence, KS 35 (1.0) $8 \times 5 - 4 - 1$ Steve Wilson, 6/21Lawrence, KS 36 (1.0) $8 \times 5 - 4 \times 1$ Jonathan Frank, 5/21Rye, NY 37 (1.0) $1 + 8 \times 5 - 4$ Steve Wilson, 6/21Lawrence, KS 38 (1.0) $8 \times 4 + 1 + 5$ Jonathan Frank, 6/21Rye, NY 39 (1.0) $(8 - 1) \times 5 + 4$ Steve Wilson, 6/21Lawrence, KS 40 (2.2) $4 \times \left(8 + \dfrac{1}{.5} \right)$ Steve Wilson, 7/21Lawrence, KS 41 (1.0) $(1 + 8) \times 5 - 4$ Steve Wilson, 7/21Lawrence, KS 42 (1.0) $8 \times \left(5 + \dfrac14 \right)$ Steve Wilson, 7/21Lawrence, KS 43 (1.0) $8 \times 5 + 4 - 1$ Jonathan Frank, 7/21Rye, NY 44 (1.0) $8 \times 5 + 4 \times 1$ Jonathan Frank, 7/21Rye, NY 45 (1.0) $8 \times 5 + 4 + 1$ Jonathan Frank, 7/21Rye, NY 46 (2.0) $54 - 8 \times 1$ Steve Wilson, 7/21Lawrence, KS 47 (2.0) $54 - 8 + 1$ Steve Wilson, 8/21Lawrence, KS 48 (1.0) $(8 + 4) \times (5 - 1)$ Jonathan Frank, 7/21Rye, NY 49 (1.0) $(8 + 1) \times 5 + 4$ Jonathan Frank, 7/21Rye, NY 50 (2.2) $48 + \dfrac{1}{.5}$ Steve Wilson, 8/21Lawrence, KS 51 (1.0) $(5 + 8) \times 4 - 1$ Jonathan Frank, 8/21Rye, NY 52 (1.0) $(5 + 8) \times 4 \times 1$ Jonathan Frank, 8/21Rye, NY 53 (1.0) $(5 + 8) \times 4 + 1$ Jonathan Frank, 8/21Rye, NY 54 (2.0) $58 - 4 \times 1$ Steve Wilson, 8/21Lawrence, KS 55 (1.0) $(8 + 4 - 1) \times 5$ Jonathan Frank, 8/21Rye, NY 56 (1.0) $(8 + 5 + 1) \times 4$ Jonathan Frank, 8/21Rye, NY 57 (2.4) $\dfrac{5}{.\overline{1}} + 4 + 8$ Steve Wilson, 10/21Lawrence, KS 58 (3.0) $58 \times 1^4$ Steve Wilson, 10/21Lawrence, KS 59 (1.0) $5 \times (8 + 4) - 1$ Steve Wilson, 8/21Lawrence, KS 60 (1.0) $5 \times (8 + 4) \times 1$ Steve Wilson, 8/21Lawrence, KS 61 (1.0) $(8 + 4) \times 5 + 1$ Jonathan Frank, 9/21Rye, NY 62 (2.0) $14 \times 5 - 8$ Jonathan Frank, 10/21Rye, NY 63 (1.0) $(8 - 1) \times (5 + 4)$ Jonathan Frank, 9/21Rye, NY 64 (1.0) $8 \times (5 + 4 - 1)$ Jonathan Frank, 9/21Rye, NY 65 (1.0) $(8 + 5) \times (4 + 1)$ Jonathan Frank, 9/21Rye, NY 66 (2.2) $\dfrac{8 \times 4 + 1}{.5}$ Jonathan Frank, 10/21Rye, NY 67 (2.0) $18 \times 4 - 5$ Jonathan Frank, 10/21Rye, NY 68 (2.0) $15 \times 4 + 8$ Jonathan Frank, 10/21Rye, NY 69 (2.0) $84 - 15$ Jonathan Frank, 10/21Rye, NY 70 (2.2) $\dfrac{8 + 4 - 5}{.1}$ Steve Wilson, 10/21Lawrence, KS 71 (1.0) $(5 + 4) \times 8 - 1$ Jonathan Frank, 11/21Rye, NY 72 (1.0) $(8 + 4) \times (5 + 1)$ Reagan MacDonald, 9/21Lawrence, KS 73 (1.0) $(5 + 4) \times 8 + 1$ Jonathan Frank, 11/21Rye, NY 74 (2.0) $14.8 \times 5$ Jonathan Frank, 11/21Rye, NY 75 (2.2) $\dfrac{15 \times 4}{.8}$ Jonathan Frank, 11/21Rye, NY 76 (2.2) $\dfrac{8 - 5}{4\%} + 1$ Steve Wilson, 11/21Lawrence, KS 77 (2.0) $18 \times 4 + 5$ Jonathan Frank, 11/21Rye, NY 78 (2.0) $84 - 5 - 1$ Steve Wilson, 11/21Lawrence, KS 79 (2.0) $84 - 5 \times 1$ Steve Wilson, 11/21Lawrence, KS 80 (1.0) $(5 + 4 + 1) \times 8$ Jonathan Frank, 12/21Rye, NY 81 (1.0) $(1 + 8) \times (5 + 4)$ Steve Wilson, 11/21Lawrence, KS 82 (2.0) $81 + 5 - 4$ Steve Wilson, 11/21Lawrence, KS 83 (2.0) $4 \times 8 + 51$ Reagan MacDonald, 9/21Lawrence, KS 84 (3.0) $84 \times 1^5$ Steve Wilson, 4/22Lawrence, KS 85 (3.0) $85 \times 1^4$ Steve Wilson, 4/22Lawrence, KS 86 (2.0) $18 \times 5 - 4$ Jonathan Frank, 12/21Rye, NY 87 (2.2) $\dfrac{4}{5\%} + 8 - 1$ Jonathan Frank, 12/21Rye, NY 88 (2.0) $84 + 5 - 1$ Satchel Koch, 10/21Lawrence, KS 89 (2.0) $85 \times 1 + 4$ Satchel Koch, 11/21Lawrence, KS 90 (2.0) $84 + 5 + 1$ Satchel Koch, 10/21Lawrence, KS 91 (2.4) $5 \times \dfrac{8}{.\overline{4}} + 1$ Jonathan Frank, 2/22Rye, NY 92 (2.0) $18.4 \times 5$ Jonathan Frank, 1/22Rye, NY 93 (3.4) $5! \times .8 - 4 + 1$ Steve Wilson, 2/22Lawrence, KS 94 (2.0) $18 \times 5 + 4$ Jonathan Frank, 12/21Rye, NY 95 (2.2) $\dfrac{48}{.5} - 1$ Jonathan Frank, 2/22Rye, NY 96 (2.2) $48 \times \dfrac{1}{.5}$ Jonathan Frank, 1/22Rye, NY 97 (2.2) $\dfrac{48}{.5} + 1$ Jonathan Frank, 1/22Rye, NY 98 (2.2) $\dfrac{5}{.1} + 48$ Jonathan Frank, 1/22Rye, NY 99 (2.0) $41 + 58$ Jonathan Frank, 12/21Rye, NY 100 (2.2) $\dfrac{8}{.1} \times \dfrac54$ J.P. Gitau, 9/21Lawrence, KS 101 (2.0) $81 + 4 \times 5$ Jonathan Frank, 1/22Rye, NY 102 (2.8) $84 + \dfrac{.1}{.\overline{5}\%}$ Steve Wilson, 3/22Lawrence, KS 103 (2.8) $\dfrac{.8}{.\overline{5}\%} - 41$ Steve Wilson, 4/22Lawrence, KS 104 (2.2) $84 + \dfrac{1}{5\%}$ Steve Wilson, 4/22Lawrence, KS 105 (2.2) $\left( \dfrac{8}{.4} + 1 \right) \times 5$ Jonathan Frank, 3/22Rye, NY 106 (3.4) $5! - 8 - (4 - 1)!$ Steve Wilson, 4/22Lawrence, KS 107 (2.0) $14 \times 8 - 5$ Jonathan Frank, 2/22Rye, NY 108 (2.2) $\dfrac{5 - 1}{4\%} + 8$ Steve Wilson, 2/22Lawrence, KS 109 (2.8) $\dfrac{1}{.\overline{8}\%} - 4 + .5$ Steve Wilson, 2/22Lawrence, KS 110 (2.0) $(14 + 8) \times 5$ Steve Wilson, 2/22Lawrence, KS 111 (3.4) $5! - 8 - \sqrt{4} + 1$ Jonathan Frank, 3/22Rye, NY 112 (3.4) $(5! - 8) \times (\sqrt{4} - 1)$ Jonathan Frank, 3/22Rye, NY 113 (3.4) $5! - 8 + \sqrt{4} - 1$ Jonathan Frank, 4/22Rye, NY 114 (3.4) $5! - 8 + 1 \times \sqrt{4}$ Jonathan Frank, 4/22Rye, NY 115 (2.2) $\dfrac{8 + 4}{.1} - 5$ Steve Wilson, 3/22Lawrence, KS 116 (2.0) $15 \times 8 - 4$ Steve Wilson, 3/22Lawrence, KS 117 (2.0) $14 \times 8 + 5$ Steve Wilson, 3/22Lawrence, KS 118 (2.2) $\dfrac{5}{4\%} - 8 + 1$ Steve Wilson, 3/22Lawrence, KS 119 (2.2) $\dfrac{8}{5\%} - 41$ Steve Wilson, 6/22Lawrence, KS 120 (1.0) $(4 - 1) \times 5 \times 8$ Anders Skjäl, 3/22Turku, Finland 121 (3.2) $5! + \dfrac84 - 1$ Jonathan Frank, 4/22Rye, NY 122 (3.2) $5! + \dfrac84 \times 1$ Jonathan Frank, 4/22Rye, NY 123 (2.0) $41 \times (8 - 5)$ Satchel Koch, 1/22Lawrence, KS 124 (2.0) $15 \times 8 + 4$ Jonathan Frank, 5/22Rye, NY 125 (2.2) $\dfrac{8 + 4}{.1} + 5$ Steve Wilson, 6/22Lawrence, KS 126 (2.0) $45 + 81$ Maddy Malm, 11/21Lawrence, KS 127 (2.6) $\dfrac{1}{.8\%} + 5 \times .4$ Steve Wilson, 5/22Lawrence, KS 128 (1.0) $(5 - 1) \times 4 \times 8$ Anders Skjäl, 3/22Turku, Finland 129 (2.4) $84 + \dfrac{5}{.\overline{1}}$ Steve Wilson, 5/22Lawrence, KS 130 (2.8) $\dfrac{1}{.\overline{5}\%} - \dfrac{4}{8\%}$ Steve Wilson, 5/22Lawrence, KS 131 (3.2) $5! + 8 + 4 - 1$ Jonathan Frank, 5/22Rye, NY 132 (2.2) $\dfrac{5}{4\%} + 8 - 1$ Jonathan Frank, 5/22Rye, NY 133 (2.2) $\dfrac{5}{4\%} + 8 \times 1$ Jonathan Frank, 5/22Rye, NY 134 (2.2) $\dfrac{8 + 5}{.1} + 4$ Steve Wilson, 5/22Lawrence, KS 135 (2.0) $84 + 51$ Satchel Koch, 10/21Lawrence, KS 136 (3.4) $5! + 1 \times 8 \times \sqrt{4}$ Steve Wilson, 6/22Lawrence, KS 137 (2.0) $145 - 8$ Steve Wilson, 5/22Lawrence, KS 138 (3.2) $5 \times 4! + 18$ Steve Wilson, 6/22Lawrence, KS 139 (2.8) $\dfrac{.8}{.\overline{5}\%} - 4 - 1$ Steve Wilson, 6/22Lawrence, KS 140 (1.0) $4 \times 5 \times (8 - 1)$ Anders Skjäl, 3/22Turku, Finland 141 (2.8) $\dfrac{.8}{.\overline{5}\%} - 4 + 1$ Steve Wilson, 7/22Lawrence, KS 142 (2.2) $\dfrac{5 + 1}{4\%} - 8$ Steve Wilson, 7/22Lawrence, KS 143 (2.0) $148 - 5$ Jonathan Frank, 6/22Rye, NY 144 (2.2) $\dfrac{18}{.5} \times 4$ Jonathan Frank, 6/22Rye, NY 145 (2.2) $\dfrac{58}{.1 \times 4}$ Jonathan Frank, 6/22Rye, NY 146 (2.0) $154 - 8$ Jonathan Frank, 6/22Rye, NY 147 (2.8) $\dfrac{.8}{.\overline{5}\%} + 4 - 1$ Steve Wilson, 7/22Lawrence, KS 148 (2.6) $\dfrac{1}{.\overline{5}\%} - 8 \times 4$ Steve Wilson, 7/22Lawrence, KS 149 (2.2) $\dfrac{8}{4\%} - 51$ Steve Wilson, 7/22Lawrence, KS 150 (2.2) $\dfrac{5 + 1}{(8 - 4)\%}$ Steve Wilson, 8/22Lawrence, KS 151 (3.2) $5! + 8 \times 4 - 1$ Jonathan Frank, 7/22Rye, NY 152 (1.0) $(4 \times 5 - 1) \times 8$ Anders Skjäl, 3/22Turku, Finland 153 (2.0) $148 + 5$ Jonathan Frank, 7/22Rye, NY 154 (2.0) $158 - 4$ Maddy Malm, 10/21Lawrence, KS 155 (1.0) $(4 \times 8 - 1) \times 5$ Anders Skjäl, 3/22Turku, Finland 156 (1.0) $(8 \times 5 - 1) \times 4$ Jonathan Frank, 7/22Rye, NY 157 (2.2) $\dfrac{8}{5\%} - 4 + 1$ Steve Wilson, 8/22Lawrence, KS 158 (2.2) $\dfrac{81}{.5} - 4$ Jonathan Frank, 7/22Rye, NY 159 (1.0) $8 \times 5 \times 4 - 1$ Reagan MacDonald, 9/21Lawrence, KS 160 (1.0) $1 \times 8 \times 5 \times 4$ J.P. Gitau, 9/21Lawrence, KS 161 (1.0) $8 \times 4 \times 5 + 1$ Satchel Koch, 2/22Lawrence, KS 162 (2.0) $158 + 4$ Jonathan Frank, 8/22Rye, NY 163 (2.2) $\dfrac{8}{5\%} + 4 - 1$ Steve Wilson, 8/22Lawrence, KS 164 (1.0) $(8 \times 5 + 1) \times 4$ Jonathan Frank, 7/22Rye, NY 165 (1.0) $(8 \times 4 + 1) \times 5$ Maddy Malm, 9/21Lawrence, KS 166 (2.2) $\dfrac{81}{.5} + 4$ Jonathan Frank, 8/22Rye, NY 167 (2.2) $\dfrac{84}{.5} - 1$ Jonathan Frank, 8/22Rye, NY 168 (1.0) $8 \times (4 \times 5 + 1)$ Steve Wilson, 9/22Lawrence, KS 169 (2.2) $\dfrac{84}{.5} + 1$ Jonathan Frank, 8/22Rye, NY 170 (2.2) $\dfrac{8 + 5 + 4}{.1}$ Steve Wilson, 8/22Lawrence, KS 171 (3.2) $85 \times \sqrt{4} + 1$ Steve Wilson, 8/22Lawrence, KS 172 (3.2) $\dfrac{(5 + 1)!}{4} - 8$ Steve Wilson, 2/23Lawrence, KS 173 (3.6) $\dfrac{5!}{\sqrt{.\overline{4}}} - 8 + 1$ Steve Wilson, 2/23Lawrence, KS 174 (2.0) $58 \times (4 - 1)$ Jonathan Frank, 9/22Rye, NY 175 (2.8) $\dfrac{1}{.\overline{5}\%} - \dfrac{4}{.8}$ Steve Wilson, 9/22Lawrence, KS 176 (2.6) $\dfrac{1}{.\overline{5}\%} - 8 + 4$ Steve Wilson, 9/22Lawrence, KS 177 (3.8) $\dfrac{1}{.\overline{5}\%} - \dfrac{4!}{8}$ Steve Wilson, 9/22Lawrence, KS 178 (2.6) $\dfrac{1}{.\overline{5}\%} - \dfrac84$ Steve Wilson, 10/22Lawrence, KS 179 (2.0) $184 - 5$ Jonathan Frank, 9/22Rye, NY 180 (1.0) $(8 + 1) \times 5 \times 4$ Jonathan Frank, 9/22Rye, NY 181 (2.0) $185 - 4$ Maddy Malm, 10/21Lawrence, KS 182 (2.0) $14 \times (8 + 5)$ Jonathan Frank, 9/22Rye, NY 183 (3.2) $185 - \sqrt{4}$ Steve Wilson, 11/22Lawrence, KS 184 (2.6) $\dfrac{1}{.\overline{5}\%} + 8 - 4$ Steve Wilson, 10/22Lawrence, KS 185 (2.2) $\dfrac{8}{4\%} - 15$ Steve Wilson, 10/22Lawrence, KS 186 (3.8) $\dfrac{1}{.\overline{5}\%} + 8 - \sqrt{4}$ Steve Wilson, 10/22Lawrence, KS 187 (3.2) $185 + \sqrt{4}$ Steve Wilson, 11/22Lawrence, KS 188 (2.4) $\dfrac{1}{.5\%} - 8 - 4$ Steve Wilson, 11/22Lawrence, KS 189 (2.0) $184 + 5$ Jonathan Frank, 9/22Rye, NY 190 (2.2) $\dfrac{81 - 5}{.4}$ Steve Wilson, 11/22Lawrence, KS 191 (3.2) $4! \times 8 - 1^5$ Steve Wilson, 2/23Lawrence, KS 192 (1.0) $8 \times 4 \times (5 + 1)$ Jonathan Frank, 10/22Rye, NY 193 (3.2) $4! \times 8 + 1^5$ Steve Wilson, 2/23Lawrence, KS 194 (2.2) $\dfrac{8}{4\%} - 5 - 1$ Jonathan Frank, 10/22Rye, NY 195 (2.2) $\left(\dfrac{8}{4\%} - 5 \right) \times 1$ Jonathan Frank, 10/22Rye, NY 196 (2.0) $51 \times 4 - 8$ Jonathan Frank, 10/22Rye, NY 197 (2.0) $41 \times 5 - 8$ Jonathan Frank, 10/22Rye, NY 198 (2.4) $\dfrac{1}{.5\%} - \dfrac84$ Steve Wilson, 11/22Lawrence, KS 199 (3.2) $\dfrac{8}{4\%} - 1^5$ Steve Wilson, 12/22Lawrence, KS 200 (1.0) $8 \times 5 \times (4 + 1)$ Jonathan Frank, 11/22Rye, NY 201 (2.2) $(41 - .8) \times 5$ Steve Wilson, 2/23Lawrence, KS 202 (2.4) $\dfrac{1}{.5\%} + \dfrac84$ Steve Wilson, 12/22Lawrence, KS 203 (3.2) $8.5 \times 4! - 1$ Steve Wilson, 4/23Lawrence, KS 204 (2.2) $\dfrac{8}{4\%} + 5 - 1$ Steve Wilson, 1/23Lawrence, KS 205 (2.2) $\dfrac{8}{4\%} + 5 \times 1$ Steve Wilson, 12/22Lawrence, KS 206 (2.2) $\dfrac{8}{4\%} + 5 + 1$ Steve Wilson, 1/23Lawrence, KS 207 (3.2) $8 \times 4! + 15$ Steve Wilson, 4/23Lawrence, KS 208 (2.2) $\dfrac{5 \times 4}{.1} + 8$ Steve Wilson, 3/23Lawrence, KS 209 (2.0) $41.8 \times 5$ Jonathan Frank, 11/22Rye, NY 210 (2.2) $\dfrac{85 - 1}{.4}$ Steve Wilson, 3/23Lawrence, KS 211 (3.2) $(8 + 1) \times 4! - 5$ Steve Wilson, 4/23Lawrence, KS 212 (2.0) $51 \times 4 + 8$ Jonathan Frank, 11/22Rye, NY 213 (3.4) $\dfrac{\sqrt{4}}{1\%} + 8 + 5$ Steve Wilson, 3/23Lawrence, KS 214 (3.4) $1.8 \times 5! - \sqrt{4}$ Steve Wilson, 4/23Lawrence, KS 215 (2.2) $\dfrac{8}{4\%} + 15$ Steve Wilson, 1/23Lawrence, KS 216 (3.2) $(5 + 1)^{4!/8}$ Steve Wilson, 3/23Lawrence, KS 217 (3.2) $\sqrt{15^4} - 8$ Steve Wilson, 4/23Lawrence, KS 218 (2.8) $\dfrac{1}{.5\%} + \dfrac{8}{.\overline{4}}$ Steve Wilson, 3/23Lawrence, KS 219 (3.6) $\dfrac{4!}{.\overline{1}} + 8 - 5$ Steve Wilson, 5/23Lawrence, KS 220 (2.2) $\dfrac{8 + 4 - 1}{5\%}$ Steve Wilson, 1/23Lawrence, KS 221 (3.2) $(8 + 1) \times 4! + 5$ Steve Wilson, 5/23Lawrence, KS 222 (3.4) $5! \times \sqrt{4} - 18$ Steve Wilson, 5/23Lawrence, KS 223 (3.4) $(5! - 8) \times \sqrt{4} - 1$ Steve Wilson, 5/23Lawrence, KS 224 (2.2) $\dfrac{14 \times 8}{.5}$ Jonathan Frank, 1/23Rye, NY 225 (3.0) $15^{8/4}$ Steve Wilson, 5/23Lawrence, KS 226 (3.4) $(5! - 8 + 1) \times \sqrt{4}$ Steve Wilson, 6/23Lawrence, KS 227 (3.4) $\dfrac{4!}{.1} - 8 - 5$ Steve Wilson, 6/23Lawrence, KS 228 (2.0) $(58 - 1) \times 4$ Steve Wilson, 6/23Lawrence, KS 229 (3.4) $\sqrt{\sqrt{15^8}} + 4$ Steve Wilson, 6/23Lawrence, KS 230 (2.2) $\dfrac{8 + 1}{4\%} + 5$ Steve Wilson, 6/23Lawrence, KS 231 (2.0) $58 \times 4 - 1$ Jonathan Frank, 11/22Rye, NY 232 (2.0) $58 \times 4 \times 1$ J.P. Gitau, 9/21Lawrence, KS 233 (2.0) $58 \times 4 + 1$ Jonathan Frank, 11/22Rye, NY 234 (3.6) $(5! - \sqrt{8 + 1}) \times \sqrt{4}$ Steve Wilson, 7/23Lawrence, KS 235 (2.0) $(48 - 1) \times 5$ Jonathan Frank, 12/22Rye, NY 236 (2.0) $(58 + 1) \times 4$ Steve Wilson, 7/23Lawrence, KS 237 (3.4) $\dfrac{4!}{.1} - 8 + 5$ Steve Wilson, 7/23Lawrence, KS 238 (2.4) $\dfrac{8 + 4 - .1}{5\%}$ Steve Wilson, 7/23Lawrence, KS 239 (2.0) $48 \times 5 - 1$ Jonathan Frank, 1/23Rye, NY 240 (2.0) $48 \times 5 \times 1$ Jonathan Frank, 1/23Rye, NY 241 (2.0) $48 \times 5 + 1$ Jonathan Frank, 1/23Rye, NY 242 (2.2) $\dfrac{8 + 4.1}{5\%}$ Steve Wilson, 7/23Lawrence, KS 243 (3.0) $(8 - 4 - 1)^5$ Steve Wilson, 8/23Lawrence, KS 244 (3.6) $\dfrac{4!}{.1} + 8 \times .5$ Steve Wilson, 8/23Lawrence, KS 245 (2.0) $(48 + 1) \times 5$ Jonathan Frank, 1/23Rye, NY 246 (3.4) $(5! - 1) \times \sqrt{4} + 8$ Steve Wilson, 8/23Lawrence, KS 247 (3.4) $5! \times \sqrt{4} + 8 - 1$ Steve Wilson, 8/23Lawrence, KS 248 (2.4) $\dfrac{1}{.5\%} + 48$ Steve Wilson, 8/23Lawrence, KS 249 (2.2) $\dfrac{5 \times 4}{8\%} - 1$ Jonathan Frank, 2/23Rye, NY 250 (2.2) $\dfrac{45}{.18}$ Jonathan Frank, 12/22Rye, NY 251 (2.2) $\dfrac{8}{4\%} + 51$ Steve Wilson, 1/23Lawrence, KS 252 (2.4) $\dfrac{5 \times 4 + 8}{.\overline{1}}$ Steve Wilson, 9/23Lawrence, KS 253 (3.4) $\dfrac{4!}{.1} + 8 + 5$ Steve Wilson, 9/23Lawrence, KS 254 (3.4) $(5! + 8 - 1) \times \sqrt{4}$ Steve Wilson, 9/23Lawrence, KS 255 (2.0) $85 \times (4 - 1)$ Jonathan Frank, 2/23Rye, NY 256 (3.0) $(5 - 4 + 1)^8$ Steve Wilson, 9/23Lawrence, KS 257 (3.2) $(5 \times .4)^8 + 1$ Steve Wilson, 9/23Lawrence, KS 258 (3.4) $(5! + 8 + 1) \times \sqrt{4}$ Steve Wilson, 10/23Lawrence, KS 259 (3.6) $\dfrac{85}{\sqrt{.\overline{1}}} + 4$ Steve Wilson, 10/23Lawrence, KS 260 (3.2) $4 \times \left( \sqrt[.5]{8} + 1 \right)$ Steve Wilson, 10/23Lawrence, KS 261 (3.2) $\sqrt{4^8} + 5 \times 1$ Steve Wilson, 10/23Lawrence, KS 262 (3.2) $\sqrt{4^8} + 5 + 1$ Steve Wilson, 10/23Lawrence, KS 263 (3.6) $\dfrac{5!}{.\overline{4}} - 8 + 1$ Steve Wilson, 11/23Lawrence, KS 264 (2.4) $\dfrac{14 - .8}{5\%}$ Steve Wilson, 2/24Lawrence, KS 265 (3.8) $\dfrac{4!}{.1} + \sqrt{\sqrt{5^8}}$ Steve Wilson, 11/23Lawrence, KS 266 (3.8) $\dfrac{(8 - 5)\%}{.\overline{1}\pmf} - 4$ Steve Wilson, 2/24Lawrence, KS 267 (3.6) $\dfrac{85 + 4}{\sqrt{.\overline{1}}}$ Steve Wilson, 11/23Lawrence, KS 268 (3.8) $\left( \dfrac{5!}{.\overline{8}} - 1\right) \times \sqrt{4}$ Steve Wilson, 2/24Lawrence, KS 269 (3.6) $\dfrac{4! + 5}{.\overline{1}} + 8$ Steve Wilson, 11/23Lawrence, KS 270 (3.8) $\dfrac{5! \times \sqrt{4} \times 1}{.\overline{8}}$ Steve Wilson, 12/23Lawrence, KS 271 (3.2) $\sqrt{4^8} + 15$ Steve Wilson, 12/23Lawrence, KS 272 (2.2) $\dfrac{14}{5\%} - 8$ Steve Wilson, 12/23Lawrence, KS 273 (3.8) $\dfrac{5!}{.\overline{4}} + \sqrt{8 + 1}$ Steve Wilson, 2/24Lawrence, KS 274 (3.6) $\dfrac{4!}{.\overline{1}} + 58$ Steve Wilson, 12/23Lawrence, KS 275 (3.6) $\dfrac{4! - \dfrac{1}{.5}}{8\%}$ Steve Wilson, 2/24Lawrence, KS 276 (3.4) $(5! + 18) \times \sqrt{4}$ Steve Wilson, 12/23Lawrence, KS 277 (3.6) $\dfrac{5!}{.\overline{4}} + 8 - 1$ Steve Wilson, 1/24Lawrence, KS 278 (3.6) $\dfrac{5!}{.\overline{4}} + 8 \times 1$ Steve Wilson, 1/24Lawrence, KS 279 (3.6) $\dfrac{5!}{.\overline{4}} + 8 + 1$ Steve Wilson, 1/24Lawrence, KS 280 (2.2) $\dfrac{18 - 4}{5\%}$ Steve Wilson, 1/24Lawrence, KS 281 (3.8) $\sqrt{\dfrac{\sqrt{4}}{5\%\pmf}} + 81$ Steve Wilson, 3/24Lawrence, KS 282 (3.4) $\dfrac{4! + 5}{.1} - 8$ Steve Wilson, 3/24Lawrence, KS 283 (2.4) $\dfrac{8 \times 4}{.\overline{1}} - 5$ Steve Wilson, 1/24Lawrence, KS 284 (2.4) $\dfrac{1}{.5\%} + 84$ Steve Wilson, 3/24Lawrence, KS 285 (3.4) $\dfrac{\sqrt{4}}{1\%} + 85$ Steve Wilson, 3/24Lawrence, KS 286 (3.8) $\dfrac{4! - 5!\%}{8\%} + 1$ Steve Wilson, 3/24Lawrence, KS 287 (3.6) $\dfrac{4! - 1}{8\%} - .5$ Steve Wilson, 4/24Lawrence, KS 288 (2.0) $48 \times (5 + 1)$ Jonathan Frank, 2/23Rye, NY 289 (3.4) $\sqrt[.5]{4! - 8 + 1}$ Steve Wilson, 4/24Lawrence, KS 290 (2.0) $58 \times (4 + 1)$ Jonathan Frank, 2/23Rye, NY 291 (3.4) $\dfrac{58}{\sqrt{4\%}} + 1$ Steve Wilson, 4/24Lawrence, KS 292 (3.4) $\dfrac{5 + 1}{(\sqrt{4})\%} - 8$ Steve Wilson, 4/24Lawrence, KS 293 (2.4) $\dfrac{8 \times 4}{.\overline{1}} + 5$ Steve Wilson, 4/24Lawrence, KS 294 (3.4) $\dfrac{4!}{8\%} - 5 - 1$ Steve Wilson, 5/24Lawrence, KS 295 (3.4) $\dfrac{4!}{8\%} - 5 \times 1$ Steve Wilson, 5/24Lawrence, KS 296 (2.2) $\dfrac{148}{.5}$ Jonathan Frank, 3/23Rye, NY 297 (3.8) $\dfrac{4! - (5 - 1)!\%}{8\%}$ Steve Wilson, 5/24Lawrence, KS 298 (3.4) $\dfrac{4!}{.1} + 58$ Steve Wilson, 5/24Lawrence, KS 299 (3.4) $\dfrac{4!}{8\%} - 1^5$ Steve Wilson, 5/24Lawrence, KS 300 (2.2) $\dfrac{54}{.18}$ Jonathan Frank, 12/22Rye, NY 301 (3.4) $\dfrac{4!}{8\%} + 1^5$ Steve Wilson, 6/24Lawrence, KS 302 (2.8) $\dfrac{.4}{.\overline{1}\%} - 58$ Steve Wilson, 6/24Lawrence, KS 303 (3.6) $\dfrac{5!}{.4} + \sqrt{8 + 1}$ Steve Wilson, 6/24Lawrence, KS 304 (2.0) $(81 - 5) \times 4$ Steve Wilson, 6/24Lawrence, KS 305 (3.4) $\dfrac{4!}{8\%} + 5 \times 1$ Steve Wilson, 6/24Lawrence, KS 315 (2.0) $45 \times (8 - 1)$ Jonathan Frank, 3/23Rye, NY 319 (2.0) $81 \times 4 - 5$ Jonathan Frank, 3/23Rye, NY 320 (2.2) $\dfrac{48}{.15}$ Jonathan Frank, 3/23Rye, NY 323 (2.0) $41 \times 8 - 5$ Satchel Koch, 1/22Lawrence, KS 326 (2.2) $815 \times .4$ Jonathan Frank, 3/23Rye, NY 329 (2.0) $81 \times 4 + 5$ Jonathan Frank, 4/23Rye, NY 332 (2.0) $41.5 \times 8$ Jonathan Frank, 4/23Rye, NY 333 (2.0) $41 \times 8 + 5$ Jonathan Frank, 4/23Rye, NY 336 (2.0) $(85 - 1) \times 4$ Jonathan Frank, 4/23Rye, NY 339 (2.0) $85 \times 4 - 1$ Jonathan Frank, 5/23Rye, NY 340 (2.0) $85 \times 4 \times 1$ Maddy Malm, 9/21Lawrence, KS 341 (2.0) $85 \times 4 + 1$ Jonathan Frank, 5/23Rye, NY 359 (2.0) $45 \times 8 - 1$ Jonathan Frank, 5/23Rye, NY 360 (2.0) $18 \times 5 \times 4$ Jonathan Frank, 5/23Rye, NY 361 (2.0) $45 \times 8 + 1$ Jonathan Frank, 5/23Rye, NY 368 (2.2) $\dfrac{184}{.5}$ Jonathan Frank, 6/23Rye, NY 381 (3.2) $81 \times 5 - 4!$ Jonathan Frank, 5/23Rye, NY 384 (3.2) $51 \times 8 - 4!$ Jonathan Frank, 5/23Rye, NY 387 (2.2) $\dfrac{4}{1\%} - 8 - 5$ Jonathan Frank, 5/23Rye, NY 396 (2.2) $\dfrac{8 \times 5}{.1} - 4$ Jonathan Frank, 4/23Rye, NY 397 (2.2) $\dfrac{4}{1\%} - 8 + 5$ Jonathan Frank, 5/23Rye, NY 398 (3.4) $\dfrac{8 \times 5}{.1} - \sqrt{4}$ Jonathan Frank, 12/22Rye, NY 400 (2.4) $\dfrac{8}{.4 \times 1 \times 5\%}$ Jonathan Frank, 12/22Rye, NY 401 (2.0) $81 \times 5 - 4$ Jonathan Frank, 7/23Rye, NY 403 (3.2) $81 \times 5 - \sqrt{4}$ Jonathan Frank, 7/23Rye, NY 404 (2.0) $51 \times 8 - 4$ Jonathan Frank, 7/23Rye, NY 405 (3.2) $45 \times \sqrt{81}$ Jonathan Frank, 4/24Rye, NY 406 (3.2) $51 \times 8 - \sqrt{4}$ Jonathan Frank, 7/23Rye, NY 407 (3.2) $81 \times 5 + \sqrt{4}$ Jonathan Frank, 7/23Rye, NY 409 (2.0) $81 \times 5 + 4$ Jonathan Frank, 8/23Rye, NY 410 (3.2) $51 \times 8 + \sqrt{4}$ Jonathan Frank, 8/23Rye, NY 412 (2.0) $51 \times 8 + 4$ Jonathan Frank, 8/23Rye, NY 421 (2.0) $84 \times 5 + 1$ Satchel Koch, 10/21Lawrence, KS 425 (2.0) $(4 + 1) \times 85$ Satchel Koch, 11/21Lawrence, KS 429 (3.2) $81 \times 5 + 4!$ Jonathan Frank, 8/23Rye, NY 432 (2.0) $54 \times 8 \times 1$ Maddy Malm, 11/21Lawrence, KS 457 (2.0) $458 - 1$ Reagan MacDonald, 9/21Lawrence, KS 458 (3.0) $458^1$ J.P. Gitau, 2/22Lawrence, KS 459 (2.0) $458 + 1$ Carter Miller, 9/21Lawrence, KS 476 (2.0) $481 - 5$ J.P. Gitau, 2/22Lawrence, KS 484 (2.0) $485 - 1$ Jonathan Frank, 4/24Rye, NY 485 (2.0) $485 \times 1$ Jonathan Frank, 4/24Rye, NY 486 (2.0) $485 + 1$ Jonathan Frank, 4/24Rye, NY 494 (3.2) $518 - 4!$ Jonathan Frank, 8/23Rye, NY 506 (2.0) $514 - 8$ Kevin McDonald, 1/22Birmingham, AL 514 (2.0) $518 - 4$ Jonathan Frank, 9/23Rye, NY 516 (3.2) $518 - \sqrt{4}$ Jonathan Frank, 9/23Rye, NY 520 (3.2) $518 + \sqrt{4}$ Jonathan Frank, 9/23Rye, NY 522 (2.0) $518 + 4$ Jonathan Frank, 9/23Rye, NY 506 (2.0) $514 - 8$ Kevin McDonald, 1/22Birmingham, AL 542 (3.2) $518 + 4!$ Jonathan Frank, 9/23Rye, NY 544 (3.0) $5^4 - 81$ Jonathan Frank, 10/23Rye, NY 547 (2.0) $548 - 1$ Maddy Malm, 10/21Lawrence, KS 548 (2.0) $548 \times 1$ Satchel Koch, 12/21Lawrence, KS 549 (2.0) $548 + 1$ Satchel Koch, 12/21Lawrence, KS 557 (3.2) $581 - 4!$ Jonathan Frank, 10/23Rye, NY 577 (2.0) $581 - 4$ J.P. Gitau, 2/22Lawrence, KS 579 (3.2) $581 - \sqrt{4}$ Jonathan Frank, 10/23Rye, NY 583 (2.0) $584 - 1$ Maddy Malm, 11/21Lawrence, KS 584 (2.0) $584 \times 1$ Satchel Koch, 12/21Lawrence, KS 585 (2.0) $584 + 1$ Satchel Koch, 12/21Lawrence, KS 605 (3.2) $581 + 4!$ Jonathan Frank, 10/23Rye, NY 607 (3.0) $5^4 - 18$ Jonathan Frank, 10/23Rye, NY 616 (3.0) $5^4 - 8 - 1$ Satchel Koch, 2/22Lawrence, KS 617 (3.0) $5^4 - 8^1$ J.P. Gitau, 12/21Lawrence, KS 618 (3.0) $5^4 - 8 + 1$ Satchel Koch, 2/22Lawrence, KS 632 (3.0) $5^4 + 8 - 1$ Jonathan Frank, 11/23Rye, NY 633 (3.0) $5^4 + 8 \times 1$ Jonathan Frank, 11/23Rye, NY 634 (3.0) $5^4 + 8 + 1$ Jonathan Frank, 11/23Rye, NY 643 (3.0) $5^4 + 18$ Jonathan Frank, 11/23Rye, NY 706 (3.0) $5^4 + 81$ Satchel Koch, 1/22Lawrence, KS 720 (2.0) $15 \times 48$ Jonathan Frank, 4/24Rye, NY 740 (2.0) $148 \times 5$ Satchel Koch, 12/21Lawrence, KS 809 (2.0) $814 - 5$ Maddy Malm, 11/21Lawrence, KS 810 (2.0) $18 \times 45$ Jonathan Frank, 4/24Rye, NY 811 (2.0) $815 - 4$ J.P. Gitau, 2/22Lawrence, KS 812 (2.0) $14 \times 58$ Jonathan Frank, 4/24Rye, NY 845 (2.0) $845 \times 1$ Jonathan Frank, 12/23Rye, NY 847 (2.0) $851 - 4$ Kevin McDonald, 1/22Birmingham, AL 853 (2.0) $854 - 1$ Carter Miller, 9/21Lawrence, KS 854 (2.0) $854 \times 1$ Jonathan Frank, 12/23Rye, NY 943 (3.0) $4^5 - 81$ Jonathan Frank, 12/23Rye, NY 972 (2.0) $18 \times 54$ Maddy Malm, 11/21Lawrence, KS 1006 (3.0) $4^5 - 18$ Jonathan Frank, 12/23Rye, NY 1015 (3.0) $4^5 - 8 - 1$ Jonathan Frank, 12/23Rye, NY 1016 (3.0) $4^5 - 8^1$ Reagan MacDonald, 9/21Lawrence, KS 1017 (3.0) $4^5 + 1 - 8$ Jonathan Frank, 1/24Rye, NY 1031 (3.0) $4^5 - 1 + 8$ Jonathan Frank, 1/24Rye, NY 1032 (3.0) $4^5 + 1 \times 8$ Jonathan Frank, 1/24Rye, NY 1033 (3.0) $4^5 + 1 + 8$ Jonathan Frank, 1/24Rye, NY 1042 (3.0) $4^5 + 18$ Jonathan Frank, 1/24Rye, NY 1076 (3.4) $\sqrt{81} \times 5! - 4$ Jonathan Frank, 6/24Rye, NY 1078 (3.6) $\sqrt{81} \times 5! - \sqrt{4}$ Jonathan Frank, 6/24Rye, NY 1105 (3.0) $4^5 + 81$ Jonathan Frank, 2/24Rye, NY 1190 (2.0) $14 \times 85$ Jonathan Frank, 4/24Rye, NY 1260 (2.0) $84 \times 15$ J.P. Gitau, 12/21Lawrence, KS 1458 (2.0) $1458$ Satchel Koch, 1/22Lawrence, KS 1485 (2.0) $1485$ Jonathan Frank, 3/24Rye, NY 1548 (2.0) $1548$ Satchel Koch, 1/22Lawrence, KS 1584 (2.0) $1584$ Jonathan Frank, 3/24Rye, NY 1632 (2.0) $51 \times 8 \times 4$ Kevin McDonald, 1/22Birmingham, AL 1845 (2.0) $1845$ Jonathan Frank, 2/24Rye, NY 1854 (2.0) $1854$ J.P. Gitau, 12/21Lawrence, KS 2378 (2.0) $41 \times 58$ Jonathan Frank, 5/24Rye, NY 2448 (2.0) $48 \times 51$ Jonathan Frank, 5/24Rye, NY 3485 (2.0) $41 \times 85$ Carter Miller, 5/22Lawrence, KS 3645 (2.0) $45 \times 81$ Jonathan Frank, 5/24Rye, NY 4045 (3.0) $8^4 - 51$ Satchel Koch, 11/21Lawrence, KS 4111 (3.0) $8^4 + 15$ Maddy Malm, 2/22Lawrence, KS 4147 (3.0) $8^4 + 51$ Satchel Koch, 11/21Lawrence, KS 4158 (2.0) $4158$ Jonathan Frank, 3/24Rye, NY 4185 (2.0) $4185$ Jonathan Frank, 3/24Rye, NY 4284 (2.0) $51 \times 84$ Jonathan Frank, 5/24Rye, NY 4328 (2.0) $541 \times 8$ Carter Miller, 5/22Lawrence, KS 4374 (2.0) $54 \times 81$ Jonathan Frank, 5/24Rye, NY 4518 (2.0) $4518$ Jonathan Frank, 3/24Rye, NY 4581 (2.0) $4581$ Jonathan Frank, 6/24Rye, NY 4815 (2.0) $4815$ Jonathan Frank, 6/24Rye, NY 4851 (2.0) $4851$ Jonathan Frank, 6/24Rye, NY 5000 (3.0) $5^4 \times 8 \times 1$ Jonathan Frank, 11/23Rye, NY 32727 (3.0) $8^5 - 41$ Maddy Malm, 2/22Lawrence, KS 32754 (3.0) $8^5 - 14$ J.P. Gitau, 12/21Lawrence, KS 32771 (3.2) $1 + 8^5 + \sqrt{4}$ J.P. Gitau, 2/22Lawrence, KS 32782 (3.0) $8^5 + 14$ Maddy Malm, 2/22Lawrence, KS 32809 (3.0) $8^5 + 41$ Maddy Malm, 2/22Lawrence, KS 390611 (3.0) $5^8 - 14$ J.P. Gitau, 12/21Lawrence, KS 16777216 (3.0) $8^{5 - 1 + 4}$ Maddy Malm, 2/22Lawrence, KS 268435456 (3.0) $4^{5+8+1}$ Carter Miller, 9/21Lawrence, KS 1073741824 (3.0) $8^{5+1+4}$ Carter Miller, 9/21Lawrence, KS 1220703125 (3.0) $5^{1+4+8}$ Carter Miller, 3/22Lawrence, KS 113947428721 (3.0) $581^4$ Carter Miller, 5/22Lawrence, KS 524467088401 (3.0) $851^4$ Carter Miller, 3/22Lawrence, KS 25746925826401 (3.0) $481^5$ Carter Miller, 5/22Lawrence, KS

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