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Using one copy each of the digits 2, 4, 6, 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.
Page 1 (1-400), Page 2 (401-800), Page 3 (801-1200), Page 4 (1201-1600), Page 5 (1601-2000), Page 6 (2001-2400), Page 7 (2401-2800), Page 8 (2801-16000), Page 41 (16001+).
| 2846 (2.0) $2846$ Maria Paramo Perez, 5/17 Overland Park, KS |
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| 2856 (2.0) $42 \times 68$ Hannah Maleki, 12/15 Overland Park, KS |
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| 2864 (2.0) $2864$ Maria Paramo Perez, 5/17 Overland Park, KS |
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| 2892 (2.0) $482 \times 6$ Spencer Lundquist, 1/16 Lenexa, KS |
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| 2944 (3.0) $8^2 \times 46$ Joanna Ramirez, 2/16 Olathe, KS |
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| 2976 (2.0) $48 \times 62$ Morgan Murrell, 2/16 Olathe, KS |
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| 3024 (2.6) $\dfrac{6 + 4.8\%}{.2\%}$ Steve Wilson, 2/24 Lawrence, KS |
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| 3072 (3.0) $2^6 \times 48$ Colton Tucker, 4/17 Lawrence, KS |
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| 3112 (3.6) $\left( \dfrac{8!}{6!} \right)^2 - 4!$ Nicholas Gachkar, 4/17 Overland Park, KS |
3120 (2.6) $(2 + 8\%) \times \dfrac{6}{.4\%}$ Steve Wilson, 2/24 Lawrence, KS |
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| 3132 (3.4) $\left( \dfrac{8!}{6!} \right)^2 - 4$ Stephanie Pray, 5/17 Overland Park, KS |
3140 (3.4) $\left( \dfrac{8!}{6!} \right)^2 + 4$ Stephanie Pray, 5/17 Overland Park, KS |
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| 3160 (2.4) $\dfrac{64 - .8}{2\%}$ Steve Wilson, 2/24 Lawrence, KS |
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| 3240 (2.2) $\dfrac{648}{.2}$ Feker Ashenafi, 12/16 Overland Park, KS |
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| 3304 (2.0) $826 \times 4$ Lawrence Ombasa, 2/16 Overland Park, KS |
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| 3360 (3.2) $\dfrac{8!}{6} \times \dfrac24$ Jordan May, 11/15 Overland Park, KS |
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| 3362 (3.4) $\dfrac{8! + 4!}{2 \times 6}$ Jonathan Frank, 3/21 Rye, NY |
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| 3374 (3.2) $8^4 - 6! - 2$ Waleed Saifan, 3/16 Lenexa, KS |
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| 3396 (2.2) $\dfrac{68}{2\%} - 4$ Jonathan Frank, 11/21 Rye, NY |
3398 (2.4) $\dfrac{68 - 4\%}{2\%}$ Steve Wilson, 2/24 Lawrence, KS |
3400 (2.2) $\dfrac{68}{4\%} \times 2$ Jonathan Frank, 10/21 Rye, NY |
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| 3402 (2.4) $\dfrac{68 + 4\%}{2\%}$ Steve Wilson, 2/24 Lawrence, KS |
3404 (2.2) $\dfrac{68}{2\%} + 4$ Jonathan Frank, 10/21 Rye, NY |
3408 (2.0) $426 \times 8$ Khat Reeves, 10/15 Lenexa, KS |
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| 3448 (2.0) $862 \times 4$ Callie Biddle, 1/16 Olathe, KS |
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| 3612 (2.0) $86 \times 42$ Adam Alazzeh, 11/15 Overland Park, KS |
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| 3696 (2.0) $462 \times 8$ Joanna Ramirez, 5/16 Olathe, KS |
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| 3750 (2.4) $\dfrac{6 \times 2}{4\% \times 8\%}$ Yi Zheng, 2/16 Olathe, KS |
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| 3772 (2.0) $46 \times 82$ Lawrence Ombasa, 2/16 Overland Park, KS |
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| 3840 (3.0) $4^6 - 2^8$ Mahmoud Albadawi, 3/16 Overland Park, KS |
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| 3844 (3.0) $62^{8/4}$ Jonathan Frank, 8/21 Rye, NY |
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| 3875 (2.8) $\dfrac{ \dfrac{6}{.\overline{2}} + 4}{.8\%}$ Steve Wilson, 2/24 Lawrence, KS |
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| 3999 (2.8) $\dfrac{8 + .6\%}{.2\%} - 4$ Steve Wilson, 2/24 Lawrence, KS |
4000 (2.2) $(4 + 6) \times \dfrac{8}{2\%}$ Morgan Murrell, 2/16 Olathe, KS |
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| 4032 (2.6) $\dfrac{8 + 6.4\%}{.2\%}$ Steve Wilson, 2/24 Lawrence, KS |
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| 4060 (2.6) $\dfrac{4 + 6\%}{(8 + 2)\%\%}$ Steve Wilson, 2/24 Lawrence, KS |
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| 4088 (3.0) $64^2 - 8$ Spencer Lundquist, 2/16 Lenexa, KS |
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| 4092 (3.0) $8^4 - 6 + 2$ Waleed Saifan, 3/16 Lenexa, KS |
4093 (3.0) $8^4 - \dfrac62$ Mahmoud Albadawi, 3/16 Overland Park, KS |
4094 (3.2) $\left( \dfrac{8}{\sqrt{4}} \right)^6 - 2$ Nicholas Gachkar, 2/17 Overland Park, KS |
4096 (3.0) $8^2 \times 64$ Khat Reeves, 11/15 Lenexa, KS |
4098 (3.2) $\left( \dfrac{8}{\sqrt{4}} \right)^6 + 2$ Nicholas Gachkar, 2/17 Overland Park, KS |
4099 (3.0) $8^4 + \dfrac62$ Mahmoud Albadawi, 3/16 Overland Park, KS |
4100 (2.2) $\dfrac{82}{(6 - 4)\%}$ Steve Wilson, 2/24 Lawrence, KS |
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| 4102 (3.0) $4^6 + 8 - 2$ Hannah Maleki, 10/15 Overland Park, KS |
4104 (3.0) $64^2 + 8$ Jessica Hodge, 1/16 Overland Park, KS |
4108 (3.0) $8^4 + 2 \times 6$ Abigail Bishop, 9/15 Olathe, KS |
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| 4128 (3.2) $86 \times 4! \times 2$ Katrina Balman, 5/16 Olathe, KS |
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| 4132 (3.0) $8^4 + 6^2$ Taryn Blanchard, 9/15 Lawrence, KS |
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| 4158 (3.0) $8^4 + 62$ Salvador Aguirre, 8/16 Overland Park, KS |
4160 (2.6) $\dfrac{ \dfrac{2}{8\%\%} - 4}{.6}$ Steve Wilson, 2/24 Lawrence, KS |
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| 4178 (3.0) $4^6 + 82$ Salvador Aguirre, 8/16 Overland Park, KS |
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| 4230 (2.2) $\dfrac{846}{.2}$ Jacob Welsh, 5/17 Bucyrus, KS |
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| 4320 (2.2) $\dfrac{864}{.2}$ Feker Ashenafi, 12/16 Overland Park, KS |
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| 4352 (3.0) $2^8 + 4^6$ Taryn Blanchard, 10/15 Lawrence, KS |
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| 4508 (2.6) $\dfrac{6 + 4}{.\overline{2}\%} + 8$ Steve Wilson, 2/24 Lawrence, KS |
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| 4608 (3.0) $(6 \times 4)^2 \times 8$ Nathan Ostermann, 11/16 Lawrence, KS |
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| 4620 (3.0) $68^2 - 4$ Khat Reeves, 11/16 Lenexa, KS |
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| 4624 (3.0) $68^{4-2}$ Nathan Ostermann, 10/16 Lawrence, KS |
4628 (2.0) $4628$ Steve Wilson, 2/24 Lawrence, KS |
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| 4704 (3.2) $6 \times \sqrt{28^4}$ Eric Seitz, 4/17 Overland Park, KS |
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| 5040 (2.6) $\dfrac{8 \times 4.2}{.\overline{6}\%}$ Steve Wilson, 2/24 Lawrence, KS |
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| 5052 (2.0) $842 \times 6$ Callie Biddle, 1/16 Olathe, KS |
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| 5136 (2.0) $642 \times 8$ Nathan Ostermann, 1/16 McLouth, KS |
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| 5184 (3.0) $6^4 \times \dfrac82$ Jordan May, 10/15 Overland Park, KS |
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| 5208 (2.0) $84 \times 62$ Adam Alazzeh, 11/15 Overland Park, KS |
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| 5248 (2.0) $82 \times 64$ Andy Cauthon, 1/17 Shawnee, KS |
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| 5325 (2.2) $\dfrac{426}{8\%}$ Jonathan Frank, 11/22 Rye, NY |
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| 5376 (3.0) $84 \times 2^6$ Hannah Maleki, 10/16 Overland Park, KS |
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| 5408 (3.2) $8 \times \sqrt{26^4}$ Eric Seitz, 5/17 Overland Park, KS |
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| 5760 (2.6) $\dfrac{64}{(2 - .\overline{8})\%}$ Steve Wilson, 2/24 Lawrence, KS |
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| 5776 (3.2) $8 \times (6! + 4 - 2)$ Riley Butler, 5/17 Shawnee, KS |
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| 5832 (2.8) $\dfrac{26 - 8\%}{.\overline{4}\%}$ Steve Wilson, 2/24 Lawrence, KS |
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| 6084 (3.0) $(84 - 6)^2$ Israel Olmedo, 8/16 Edgerton, KS |
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| 6144 (3.0) $2^8 \times 4 \times 6$ Nathan Ostermann, 2/16 McLouth, KS |
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| 6248 (2.0) $6248$ Maria Paramo Perez, 5/17 Overland Park, KS |
6250 (2.4) $\dfrac{6 + 4}{2\% \times 8\%}$ Jonathan Frank, 7/21 Rye, NY |
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| 6432 (3.2) $268 \times 4!$ Carsten Holtorf, 5/17 Overland Park, KS |
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| 6557 (3.0) $\left( \dfrac62 \right)^8 - 4$ Jason Alexander, 12/15 Overland Park, KS |
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| 6561 (3.0) $\left( \dfrac{6 \times 2}{4} \right)^8$ Kyle Wilkinson, 3/16 Shawnee, KS |
6565 (3.0) $\left( \dfrac62 \right)^8 + 4$ Jason Alexander, 12/15 Overland Park, KS |
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| 6672 (3.4) $\dfrac{8!}{6} - 4! \times 2$ Jonathan Frank, 11/22 Rye, NY |
6678 (2.8) $\dfrac{4 + .2\%}{6\%\%} + 8$ Steve Wilson, 2/24 Lawrence, KS |
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| 6694 (3.4) $\dfrac{8!}{6} - 4! - 2$ Jonathan Frank, 11/22 Rye, NY |
6696 (3.2) $\dfrac{8!}{6} - 24$ Jonathan Frank, 11/22 Rye, NY |
6698 (3.4) $\dfrac{8!}{6} - 4! + 2$ Jonathan Frank, 11/22 Rye, NY |
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| 6704 (3.2) $\dfrac{8!}{6} - 4^2$ Jonathan Frank, 11/22 Rye, NY |
6708 (2.6) $\dfrac{4 + 2\%}{6\%\%} + 8$ Steve Wilson, 2/24 Lawrence, KS |
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| 6712 (3.2) $\dfrac{8!}{6} - 4 \times 2$ Jonathan Frank, 11/22 Rye, NY |
6714 (2.8) $\dfrac{\dfrac{6}{.4\%} - 8}{.\overline{2}}$ Steve Wilson, 2/24 Lawrence, KS |
6718 (3.2) $\dfrac{8!}{6} - 4 + 2$ Jordan May, 12/15 Overland Park, KS |
6719 (3.4) $\dfrac{8!}{6} - \dfrac{2}{\sqrt{4}}$ Jonathan Frank, 11/22 Rye, NY |
6720 (3.4) $\dfrac{8!}{6} - 2 + \sqrt{4}$ Jonathan Frank, 11/22 Rye, NY |
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| 6721 (3.4) $\dfrac{8!}{6} + \dfrac{2}{\sqrt{4}}$ Jonathan Frank, 11/22 Rye, NY |
6722 (3.2) $\dfrac{8!}{6} + \dfrac42$ Jordan May, 11/15 Overland Park, KS |
6724 (3.0) $82^{6-4}$ Nathan Ostermann, 10/16 Lawrence, KS |
6726 (3.2) $\dfrac{8!}{6} + 4 + 2$ Jordan May, 12/15 Overland Park, KS |
6728 (3.2) $\dfrac{8!}{6} + 4 \times 2$ Jonathan Frank, 11/22 Rye, NY |
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| 6732 (2.8) $\dfrac{\dfrac{6}{.2\%} - 8}{.\overline{4}}$ Steve Wilson, 2/24 Lawrence, KS |
6736 (3.2) $\dfrac{8!}{6} + 4^2$ Jonathan Frank, 11/22 Rye, NY |
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| 6742 (2.8) $\dfrac{6}{.\overline{4} \times .2\%} - 8$ Steve Wilson, 2/24 Lawrence, KS |
6744 (3.2) $\dfrac{8!}{6} + 24$ Jonathan Frank, 11/22 Rye, NY |
6746 (3.4) $\dfrac{8!}{6} + 4! + 2$ Jonathan Frank, 11/22 Rye, NY |
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| 6762 (3.2) $\dfrac{8!}{6} + 42$ Jonathan Frank, 11/22 Rye, NY |
6768 (2.8) $\dfrac{\dfrac{6}{.2\%} + 8}{.\overline{4}}$ Steve Wilson, 2/24 Lawrence, KS |
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| 7050 (3.0) $84^2 - 6$ Spencer Lundquist, 1/16 Lenexa, KS |
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| 7056 (3.2) $84^{\sqrt{6-2}}$ Jonathan Frank, 8/21 Rye, NY |
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| 7062 (3.0) $84^2 + 6$ Spencer Lundquist, 4/16 Lenexa, KS |
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| 7200 (2.4) $\dfrac{8 + 6.4}{.2\%}$ Steve Wilson, 2/24 Lawrence, KS |
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| 7392 (3.0) $86^2 - 4$ Spencer Lundquist, 3/16 Lenexa, KS |
7394 (3.2) $86^{\sqrt{4}} - 2$ Jonathan Frank, 1/22 Rye, NY |
7396 (3.0) $86^{4-2}$ Nathan Ostermann, 10/16 Lawrence, KS |
7398 (3.2) $86^{\sqrt{4}} + 2$ Jonathan Frank, 1/22 Rye, NY |
7400 (2.6) $\dfrac{6 - 4 \times 2\%}{8\%\%}$ Steve Wilson, 2/24 Lawrence, KS |
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| 7776 (3.0) $(8 - 2)^4 \times 6$ Adam Shafton, 5/16 Overland Park, KS |
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| 8100 (2.6) $\dfrac{8 + 6 + 4}{.\overline{2}\%}$ Steve Wilson, 2/24 Lawrence, KS |
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| 8192 (3.0) $2^{4+6} \times 8$ Audreona Bolin, 1/16 Gardner, KS |
8198 (3.0) $8^4 \times 2 + 6$ Khat Reeves, 10/15 Lenexa, KS |
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| 8246 (2.0) $8246$ Maria Paramo Perez, 5/17 Overland Park, KS |
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| 9216 (3.0) $(8 \times 6)^2 \times 4$ Thomas Peters, 10/16 Lawrence, KS |
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| 9248 (3.2) $2 \times \sqrt{68^4}$ Jake Karst, 3/17 Overland Park, KS |
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| 9600 (2.2) $\dfrac{8 \times 6 \times 4}{2\%}$ Jacob Welsh, 4/17 Bucyrus, KS |
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| 9994 (2.4) $\dfrac{4 \times 2}{8\%\%} - 6$ Steve Wilson, 2/24 Lawrence, KS |
10000 (2.4) $\dfrac{6 + 4 - 8}{2\%\%}$ Steve Wilson, 2/24 Lawrence, KS |
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| 10006 (2.4) $\dfrac{4 \times 2}{8\%\%} + 6$ Steve Wilson, 2/24 Lawrence, KS |
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| 10083 (3.2) $\dfrac{8!}{4} + \dfrac62$ Jordan May, 10/15 Overland Park, KS |
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| 10370 (3.0) $6^4 \times 8 + 2$ Adam Alazzeh, 10/15 Overland Park, KS |
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| 11520 (3.2) $8^2 \times \dfrac{6!}{4}$ Rebecca Fowler, 3/16 Kansas City, MO |
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| 11776 (3.0) $2^8 \times 46$ Colton Tucker, 4/17 Lawrence, KS |
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| 12288 (3.0) $8^4 \times \dfrac62$ Steve Wilson, 9/21 Lawrence, KS |
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| 13824 (3.0) $48^2 \times 6$ Abigail Bishop, 9/15 Olathe, KS |
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| 14641 (3.0) $\left( 8 + \dfrac62 \right)^4$ Jonathan Frank, 11/22 Rye, NY |
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| 14792 (3.2) $2 \times \sqrt{86^4}$ Hamza Damer, 3/17 Lenexa, KS |
Page 1 (1-400), Page 2 (401-800), Page 3 (801-1200), Page 4 (1201-1600), Page 5 (1601-2000), Page 6 (2001-2400), Page 7 (2401-2800), Page 8 (2801-16000), Page 41 (16001+).