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