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The first four natural numbers are 1, 2, 3, and 4. Create each of the positive integers using one copy of each number, and any standard operations. 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+)
| 1625 (2.4) $\dfrac{3 + \dfrac14 }{.2\%}$ Jordan Pfeiffer, 6/12 Mission Woods, KS |
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| 1678 (3.0) $41^2 - 3$ Aimee Shupe, 7/09 Lenexa, KS |
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| 1684 (3.0) $41^2 + 3$ Scott Dixon, 10/07 Lenexa, KS |
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| 1700 (2.2) $\dfrac{34}{2 \times 1\%}$ Kellen Horsfall, 7/12 Lawrence, KS |
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| 1701 (3.0) $3^4 \times 21$ Elizabeth Waters, 7/12 Lawrence, KS |
1705 (2.2) $\dfrac{341}{.2}$ Jason Cosentino, 6/12 Lawrence, KS |
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| 1724 (3.0) $12^3 - 4$ Alan Cooke, 8/10 Prairie Village, KS |
1728 (3.0) $(14 - 2)^3$ Tien Huynh, 10/10 Olathe, KS |
1729 (3.2) $\left( \dfrac{4!}{2} \right)^3 + 1$ Steve Wilson, 7/22 Lawrence, KS |
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| 1732 (3.0) $12^3 + 4$ Alan Cooke, 8/10 Prairie Village, KS |
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| 1750 (3.2) $\dfrac{14}{.2^3}$ Jack Brewer, 9/12 Mission, KS |
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| 1764 (3.0) $(14 \times 3)^2$ Michele Gaston, 12/10 Olathe, KS |
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| 1848 (3.0) $43^2 - 1$ Eric Millard, 5/07 Olathe, KS |
1849 (3.0) $43^2 \times 1$ Tiffany Copple, 2/07 Overland Park, KS |
1850 (3.0) $43^2 + 1$ Melissa Kuskowski, 4/07 Olathe, KS |
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| 1920 (3.4) $\dfrac{4!^2}{3 \times .1}$ Gongda Fang, 7/12 Lawrence, KS |
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| 1922 (3.2) $31^2 \times \sqrt{4}$ Stacey Henry, 9/10 Overland Park, KS |
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| 1936 (3.0) $(41 + 3)^2$ John Hepfer, 11/07 Shawnee, KS |
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| 1996 (3.2) $\dfrac{2}{.1^3} - 4$ Gongda Fang, 7/12 Lawrence, KS |
1997 (3.4) $\dfrac{.2}{.1^4} - 3$ Gongda Fang, 7/12 Lawrence, KS |
2000 (3.2) $\dfrac{ \left( \dfrac{2}{.1} \right)^3}{4}$ Kenneth Chapman, 5/10 Santa Paula, CA |
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| 2048 (3.0) $\dfrac{2^{13}}{4}$ Mary Tuggle, 8/09 Kansas City, MO |
2049 (3.2) $\dfrac{4^{3!}}{2} + 1$ Matthew Stevens, 4/10 Overland Park, KS |
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| 2134 (2.0) $2134$ David Jamison, 11/10 Lawrence, KS |
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| 2143 (2.0) $2143$ David Jamison, 11/10 Lawrence, KS |
2150 (2.2) $\dfrac{43}{2 \times 1\%}$ Katie Roberts, 6/12 Washington, DC |
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| 2250 (3.2) $\dfrac{1}{4 \pmf} \times 3^2$ Junjie Mao, 6/12 Lawrence, KS |
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| 2314 (2.0) $2314$ David Jamison, 11/10 Lawrence, KS |
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| 2340 (2.2) $\dfrac{234}{.1}$ Jason Cosentino, 6/12 Lawrence, KS |
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| 2341 (2.0) $2341$ David Jamison, 11/10 Lawrence, KS |
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| 2400 (3.4) $(2 + 1) \times \dfrac{4!}{3\%}$ Kellen Horsfall, 7/12 Lawrence, KS |
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| 2401 (3.0) $\left( \dfrac{21}{3} \right)^4$ Tien Huynh, 9/10 Olathe, KS |
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| 2413 (2.0) $2413$ David Jamison, 10/10 Lawrence, KS |
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| 2472 (3.2) $412 \times 3!$ Sara Stites, 7/12 Lawrence, KS |
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| 2526 (3.2) $421 \times 3!$ Shannon O'Neill, 6/12 Lawrence, KS |
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| 2704 (3.0) $(13 \times 4)^2$ Tien Huynh, 9/10 Olathe, KS |
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| 2742 (3.0) $14^3 - 2$ John Hepfer, 11/07 Shawnee, KS |
2746 (3.0) $14^3 + 2$ Tina Redlinger, 10/07 Olathe, KS |
2750 (2.4) $\dfrac{2 + \dfrac34}{.1\%}$ Katie Roberts, 6/12 Washington, DC |
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| 2879 (3.2) $(3 \times 2)! \times 4 - 1$ Harman Tiwana, 11/12 Lenexa, KS |
2880 (3.4) $4 \times (\sqrt{12 \times 3})!$ Cooper Krause, 6/12 Lawrence, KS |
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| 2881 (3.2) $(3 \times 2)! \times 4 + 1$ Harman Tiwana, 11/12 Lenexa, KS |
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| 2952 (3.2) $123 \times 4!$ Ben Kerkhoff, 7/12 Lawrence, KS |
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| 3024 (3.4) $4! \times 3! \times 21$ Tien Huynh, 12/10 Olathe, KS |
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| 3075 (2.2) $\dfrac{123}{4\%}$ Pierre LeGrange, 10/08 Overland Park, KS |
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| 3124 (2.0) $3124$ David Jamison, 12/10 Lawrence, KS |
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| 3142 (2.0) $3142$ David Jamison, 12/10 Lawrence, KS |
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| 3168 (3.2) $132 \times 4!$ Elizabeth Waters, 7/12 Lawrence, KS |
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| 3200 (3.2) $2^3 \times \dfrac{4}{1\%}$ Brett Wolverton, 10/10 Overland Park, KS |
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| 3201 (3.2) $\dfrac{4^3}{2\%} + 1$ Larry Flanagan, 6/12 Lawrence, KS |
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| 3214 (2.0) $3214$ David Jamison, 12/10 Lawrence, KS |
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| 3241 (2.0) $3241$ David Jamison, 12/10 Lawrence, KS |
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| 3300 (2.2) $\dfrac{132}{4\%}$ Melissa Heller, 10/08 Overland Park, KS |
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| 3412 (2.0) $3412$ David Jamison, 12/10 Lawrence, KS |
3420 (2.2) $\dfrac{342}{.1}$ Jason Cosentino, 6/12 Lawrence, KS |
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| 3421 (2.0) $3421$ Bruno Biazetto, 5/17 Overland Park, KS |
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| 3455 (3.4) $4!^2 \times 3! - 1$ Tami Lawler-Bontrager, 11/07 Overland Park, KS |
3456 (3.4) $4!^2 \times 3! \times 1$ Dominic Clemente, 6/12 Lawrence, KS |
3457 (3.4) $4!^2 \times 3! + 1$ Dominic Clemente, 6/12 Lawrence, KS |
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| 3500 (3.6) $\dfrac{2}{1 \pmf} + \dfrac{3!}{4 \pmf}$ Junjie Mao, 6/12 Lawrence, KS |
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| 3600 (3.4) $\dfrac{3!^{4/2}}{1\%}$ Tami Lawler-Bontrager, 11/07 Overland Park, KS |
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| 3844 (3.0) $31^2 \times 4$ Scott Dixon, 12/07 Lenexa, KS |
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| 4032 (3.4) $\left( \dfrac{32}{4} \right)! \times .1$ Cooper Krause, 6/12 Lawrence, KS |
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| 4056 (3.2) $13^2 \times 4!$ Brianne Goldston, 7/12 Cheney, KS |
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| 4093 (3.2) $4^{3!} - 2 - 1$ Matthew Stevens, 4/10 Overland Park, KS |
4094 (3.2) $4^{3!} - 2 \times 1$ Matthew Stevens, 4/10 Overland Park, KS |
4095 (3.0) $4^{3 \times 2} - 1$ Scott Dixon, 12/07 Lenexa, KS |
4096 (3.0) $4^{3 \times 2} \times 1$ Scott Dixon, 12/07 Lenexa, KS |
4097 (3.0) $4^{3 \times 2} + 1$ Scott Dixon, 12/07 Lenexa, KS |
4099 (3.2) $4^3! + 2 + 1$ Sara Stites, 6/12 Lawrence, KS |
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| 4108 (3.2) $4^3! + 12$ Sara Stites, 6/12 Lawrence, KS |
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| 4117 (3.2) $4^3! + 21$ Sara Stites, 6/12 Lawrence, KS |
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| 4123 (2.0) $4123$ Sara Stites, 6/12 Lawrence, KS |
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| 4225 (3.2) $\dfrac{13^2}{4\%}$ Brett Wolverton, 10/10 Overland Park, KS |
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| 4231 (2.0) $4231$ Haoyuan Wu, 6/12 Lawrence, KS |
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| 4302 (2.2) $\dfrac{43}{1\%} + 2$ Brianne Goldston, 7/12 Cheney, KS |
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| 4320 (2.2) $\dfrac{432}{.1}$ Jason Cosentino, 6/12 Lawrence, KS |
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| 4321 (2.0) $4321$ Haoyuan Wu, 6/12 Lawrence, KS |
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| 4800 (3.2) $4^2 \times \dfrac{3}{1\%}$ Brett Wolverton, 10/10 Overland Park, KS |
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| 4913 (3.0) $(21 - 4)^3$ Tien Huynh, 11/10 Olathe, KS |
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| 5043 (3.0) $41^2 \times 3$ Scott Dixon, 10/07 Lenexa, KS |
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| 5325 (2.2) $\dfrac{213}{4\%}$ Pierre LeGrange, 10/08 Overland Park, KS |
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| 5488 (3.0) $14^3 \times 2$ Aimee Shupe, 7/09 Lenexa, KS |
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| 5544 (3.2) $231 \times 4!$ Shannon O'Neill, 6/12 Lawrence, KS |
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| 5750 (2.4) $23 \times \dfrac{1}{.4\%}$ Jordan Pfeiffer, 6/12 Mission Woods, KS |
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| 5775 (2.2) $\dfrac{231}{4\%}$ Melissa Heller, 10/08 Overland Park, KS |
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| 6000 (3.6) $(4! + 3!) \times \dfrac{2}{1\%}$ Larry Flanagan, 6/12 Lawrence, KS |
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| 6398 (3.2) $\dfrac{4^3}{1\%} - 2$ Li-Yu Chen, 7/12 Lawrence, KS |
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| 6402 (3.2) $\dfrac{4^3}{1\%} + 2$ Li-Yu Chen, 7/12 Lawrence, KS |
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| 6560 (3.0) $3^{4 \times 2} - 1$ Eric Anderson, 9/09 Overland Park, KS |
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| 6561 (3.0) $(3 \times 1)^{4 \times 2}$ Eric Anderson, 8/09 Overland Park, KS |
6562 (3.0) $3^{4 \times 2} + 1$ Eric Anderson, 8/09 Overland Park, KS |
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| 6700 (2.2) $\dfrac{134}{2\%}$ Pierre LeGrange, 10/08 Overland Park, KS |
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| 6912 (3.0) $\dfrac{12^4}{3}$ Tiffany Copple, 2/07 Overland Park, KS |
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| 7150 (2.2) $\dfrac{143}{2\%}$ Stacey Henry, 9/10 Overland Park, KS |
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| 7200 (2.2) $24 \times \dfrac{3}{1\%}$ Mary A. M., 8/12 Overland Park, KS |
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| 7704 (3.2) $321 \times 4!$ Nick Evans, 6/12 Lawrence, KS |
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| 7800 (2.2) $\dfrac{312}{4\%}$ Pierre LeGrange, 10/08 Overland Park, KS |
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| 8025 (2.2) $\dfrac{321}{4\%}$ Melissa Heller, 10/08 Overland Park, KS |
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| 8098 (3.2) $\dfrac{3^4}{1\%} - 2$ Li-Yu Chen, 7/12 Lawrence, KS |
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| 8102 (3.2) $\dfrac{3^4}{1\%} + 2$ Larry Flanagan, 6/12 Lawrence, KS |
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| 8188 (3.0) $2^{13} - 4$ Michael Freeman, 12/10 Merriam, KS |
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| 8194 (3.2) $\sqrt{4^{13}} + 2$ Rabeh Ghadiri, 10/08 Overland Park, KS |
8196 (3.0) $2^{13} + 4$ Michael Freeman, 12/10 Merriam, KS |
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| 8640 (3.6) $\dfrac{(3!)! \times 4!}{2 \times 1}$ Jack Brewer, 9/12 Mission, KS |
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| 9200 (2.2) $23 \times \dfrac{4}{1\%}$ Mary A. M., 8/12 Overland Park, KS |
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| 9257 (3.0) $21^3 - 4$ Scott Dixon, 11/07 Lenexa, KS |
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| 9265 (3.0) $21^3 + 4$ Scott Dixon, 11/07 Lenexa, KS |
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| 9285 (3.2) $21^3 + 4!$ Samantha Maupin, 6/12 Lawrence, KS |
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| 10080 (3.2) $(3 \times 2)! \times 14$ Cooper Krause, 6/12 Lawrence, KS |
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| 10086 (3.2) $41^2 \times 3!$ Dominic Clemente, 6/12 Lawrence, KS |
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| 12600 (2.2) $42 \times \dfrac{3}{1\%}$ Mary A. M., 8/12 Overland Park, KS |
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| 12800 (3.2) $\dfrac{4^3}{1\%} \times 2$ Li-Yu Chen, 7/12 Lawrence, KS |
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| 13822 (3.2) $4!^3 - 2 \times 1$ Tien Huynh, 12/10 Olathe, KS |
13823 (3.0) $24^3 - 1$ Scott Dixon, 11/07 Lenexa, KS |
13824 (3.0) $24^3 \times 1$ John Hepfer, 10/07 Shawnee, KS |
13825 (3.0) $24^3 + 1$ Scott Dixon, 11/07 Lenexa, KS |
13826 (3.2) $4!^3 + 2 \times 1$ Margo Shoopman, 8/09 Kansas City, MO |
13827 (3.2) $4!^3 + 2 + 1$ Margo Shoopman, 8/09 Kansas City, MO |
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| 14400 (3.2) $\dfrac{(4 \times 3)^2}{1\%}$ Michelle Spencer, 7/11 Harrisonville, MO |
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| 15129 (3.0) $(41 \times 3)^2$ Ambra Robinson, 1/11 Lawrence, KS |
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| 15625 (3.0) $(21 + 4)^3$ Tien Huynh, 11/10 Olathe, KS |
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| 15700 (2.2) $\dfrac{314}{2\%}$ Melissa Heller, 10/08 Overland Park, KS |
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| 16200 (3.2) $3^4 \times \dfrac{2}{1\%}$ Larry Flanagan, 7/12 Lawrence, KS |
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| 16381 (3.0) $2^{14} - 3$ Chris Harris, 7/12 Overland Park, KS |
16387 (3.0) $2^{14} + 3$ Chris Harris, 7/12 Overland Park, KS |
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| 17050 (2.2) $\dfrac{341}{2\%}$ Pierre LeGrange, 10/08 Overland Park, KS |
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| 17956 (3.0) $134^2$ Jay Roath, 5/06 Overland Park, KS |
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| 18522 (3.2) $\sqrt{4} \times 21^3$ Tiffany Copple, 2/07 Overland Park, KS |
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| 20000 (3.4) $\dfrac{2^3}{1\% \times 4\%}$ Brianne Goldston, 7/12 Cheney, KS |
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| 20449 (3.0) $143^2$ Jay Roath, 5/06 Overland Park, KS |
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| 20650 (2.2) $\dfrac{413}{2\%}$ Melissa Heller, 10/08 Overland Park, KS |
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| 20733 (3.0) $12^4 - 3$ Lisa Fisher, 7/09 Lawrence, KS |
20735 (3.4) $(4! \times 3!)^2 - 1$ Tien Huynh, 12/10 Olathe, KS |
20736 (3.4) $(4! \times 3!)^2 \times 1$ Tien Huynh, 12/10 Olathe, KS |
20737 (3.4) $(4! \times 3!)^2 + 1$ Stephen Inglin, 8/09 De Soto, KS |
20739 (3.0) $12^4 + 3$ Zhenghong To, 5/10 Overland Park, KS |
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| 21550 (2.2) $\dfrac{431}{2\%}$ Umidjon Olimov, 2/11 Overland Park, KS |
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| 21952 (3.0) $(14 \times 2)^3$ Tien Huynh, 10/10 Olathe, KS |
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| 23064 (3.2) $31^2 \times 4!$ Shannon O'Neill, 6/12 Lawrence, KS |
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| 27648 (3.2) $4!^3 \times 2 \times 1$ Tien Huynh, 12/10 Olathe, KS |
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| 28559 (3.0) $13^4 - 2$ Tien Huynh, 9/10 Olathe, KS |
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| 28561 (3.2) $\sqrt{13^{4 \times 2}}$ John Hepfer, 10/07 Shawnee, KS |
28563 (3.0) $13^4 + 2$ Tien Huynh, 10/10 Olathe, KS |
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| 36000 (3.4) $3^2 \times \dfrac{4}{.1\%}$ Samantha Maupin, 7/12 Lawrence, KS |
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| 37044 (3.0) $21^3 \times 4$ Scott Dixon, 11/07 Lenexa, KS |
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| 40316 (3.2) $(4 \times 2)! - 3 - 1$ Eric Anderson, 10/09 Overland Park, KS |
40317 (3.2) $(4 \times 2 \times 1)! - 3$ Eric Anderson, 10/09 Overland Park, KS |
40318 (3.2) $(4 \times 2)! - 3 + 1$ Eric Anderson, 10/09 Overland Park, KS |
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| 40322 (3.2) $(4 \times 2)! + 3 - 1$ Eric Anderson, 10/09 Overland Park, KS |
40323 (3.2) $(4 \times 2 \times 1)! + 3$ Eric Anderson, 11/09 Overland Park, KS |
40324 (3.2) $(4 \times 2)! + 3 + 1$ Eric Anderson, 10/09 Overland Park, KS |
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| 40550 (3.6) $\dfrac{3^4 + .1}{.2\%}$ Yuncan Yang, 7/12 Lawrence, KS |
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| 41472 (3.2) $12^3 \times 4!$ Nick Evans, 6/12 Lawrence, KS |
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| 43200 (3.2) $\dfrac{12^3}{4\%}$ Larry Flanagan, 6/12 Lawrence, KS |
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| 48000 (3.4) $4^2 \times \dfrac{3}{.1\%}$ Samantha Maupin, 7/12 Lawrence, KS |
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| 49152 (3.2) $4^{3!} \times 12$ Josh Hood, 6/12 Olathe, KS |
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| 57122 (3.0) $13^4 \times 2$ Tien Huynh, 10/10 Olathe, KS |
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| 60000 (2.4) $\dfrac{4 \times 3}{2\% \times 1\%}$ Luke Sauvadon, 6/12 Lawrence, KS |
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| 60516 (3.2) $(3! \times 41)^2$ Yue Li, 6/12 Lawrence, KS |
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| 62208 (3.0) $12^4 \times 3$ Lisa Fisher, 7/09 Lawrence, KS |
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| 64827 (3.0) $\dfrac{21^4}{3}$ John Hepfer, 10/07 Shawnee, KS |
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| 68919 (3.0) $41^3 - 2$ Zhenghong To, 5/10 Overland Park, KS |
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| 68923 (3.0) $41^3 + 2$ Scott Dixon, 10/07 Lenexa, KS |
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| 69120 (3.2) $\dfrac{12^4}{.3}$ Chelsea Kiddle, 9/12 Leawood, KS |
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| 74087 (3.0) $42^3 - 1$ Melissa Kuskowski, 5/07 Olathe, KS |
74088 (3.0) $42^3 \times 1$ Melissa Kuskowski, 5/07 Olathe, KS |
74089 (3.0) $42^3 + 1$ Melissa Kuskowski, 3/07 Olathe, KS |
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| 79507 (3.0) $43^{2+1}$ John Hepfer, 11/07 Shawnee, KS |
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| 90720 (3.2) $\dfrac{(12 - 3)!}{4}$ Cooper Krause, 6/12 Lawrence, KS |
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| 98304 (3.2) $2^{14} \times 3!$ Larry Flanagan, 7/12 Lawrence, KS |
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| 98596 (3.0) $314^2$ Jay Roath, 5/06 Overland Park, KS |
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| 104976 (3.0) $(21 - 3)^4$ Tien Huynh, 9/10 Olathe, KS |
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| 114000 (3.8) $\dfrac{ \dfrac{4!}{.2} - 3!}{1\pmf}$ Steve Wilson, 7/22 Lawrence, KS |
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| 115600 (3.2) $\dfrac{34^2}{1\%}$ Denise Fernandes, 5/10 Lawrence, KS |
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| 116281 (3.0) $341^2$ Jay Roath, 5/06 Overland Park, KS |
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| 128000 (3.4) $4^3 \times \dfrac{2}{.1\%}$ Samantha Maupin, 7/12 Lawrence, KS |
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| 129600 (3.2) $\dfrac{(3\times 2)^4}{1\%}$ Stacey Henry, 9/10 Overland Park, KS |
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| 131072 (3.2) $\sqrt{ (2 \times 1)^{34}}$ Michael Freeman, 10/10 Merriam, KS |
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| 137200 (3.2) $\dfrac{14^3}{2\%}$ Denise Fernandes, 5/10 Lawrence, KS |
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| 137842 (3.0) $41^3 \times 2$ Zhenghong To, 5/10 Overland Park, KS |
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| 142805 (3.2) $\dfrac{13^4}{.2}$ Chelsea Kiddle, 9/12 Leawood, KS |
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| 162000 (3.4) $3^4 \times \dfrac{2}{.1\%}$ Samantha Maupin, 7/12 Lawrence, KS |
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| 170569 (3.0) $413^2$ Jay Roath, 5/06 Overland Park, KS |
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| 172800 (3.4) $4!^2 \times \dfrac{3}{1\%}$ Tami Lawler-Bontrager, 11/07 Overland Park, KS |
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| 180600 (5.2) $\dfrac{ {}_{43} P_2}{1\%}$ Kellen Horsfall, 7/12 Lawrence, KS |
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| 181440 (3.2) $\dfrac{(13 - 4)!}{2}$ Cooper Krause, 6/12 Lawrence, KS |
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| 184900 (3.2) $\dfrac{43^2}{1\%}$ Michelle Spencer, 7/11 Harrisonville, MO |
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| 185761 (3.0) $431^2$ Lisa Fisher, 7/09 Lawrence, KS |
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| 194487 (3.2) $21^4 + 3!$ Samantha Maupin, 6/12 Lawrence, KS |
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| 222264 (3.2) $21^3 \times 4!$ Samantha Maupin, 6/12 Lawrence, KS |
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| 231525 (3.2) $\dfrac{21^3}{4\%}$ Samantha Maupin, 6/12 Lawrence, KS |
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| 234256 (3.0) $(23 - 1)^4$ Elizabeth Waters, 7/12 Lawrence, KS |
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| 240250 (3.4) $\dfrac{31^2}{.4\%}$ Jordan Pfeiffer, 6/12 Mission Woods, KS |
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| 279840 (3.0) $23^4 - 1$ Eric Millard, 5/07 Olathe, KS |
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| 279841 (3.0) $23^4 \times 1$ Scott Dixon, 10/07 Lenexa, KS |
279842 (3.0) $23^4 + 1$ Melissa Kuskowski, 4/07 Olathe, KS |
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| 279936 (3.2) $\sqrt{(3 \times 2)^{14}}$ Michael Freeman, 10/10 Merriam, KS |
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| 290304 (3.2) $4!^3 \times 21$ Chelsea Kiddle, 9/12 Leawood, KS |
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| 320000 (3.4) $\dfrac{4^3}{2\% \times 1\%}$ Luke Sauvadon, 6/12 Lawrence, KS |
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| 331776 (3.0) $(23 + 1)^4$ Larry Flanagan, 6/12 Lawrence, KS |
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| 531437 (3.0) $3^{12} - 4$ Chris Harris, 7/12 Overland Park, KS |
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| 531441 (3.2) $\sqrt{(3 \times 1)^{24}}$ Michael Freeman, 10/10 Merriam, KS |
531445 (3.0) $3^{12} + 4$ Chris Harris, 7/12 Overland Park, KS |
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| 551368 (3.0) $(41 \times 2)^3$ Scott Dixon, 9/07 Lenexa, KS |
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| 553536 (3.2) $(4! \times 31)^2$ Yue Li, 6/12 Lawrence, KS |
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| 691200 (3.2) $\dfrac{12^4}{3\%}$ Stacey Henry, 9/10 Overland Park, KS |
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| 746496 (3.2) $\dfrac{12^{3!}}{4}$ Dominic Clemente, 6/12 Lawrence, KS |
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| 923519 (3.0) $31^4 - 2$ John Hepfer, 11/07 Shawnee, KS |
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| 923523 (3.0) $31^4 + 2$ John Hepfer, 11/07 Shawnee, KS |
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| 1048575 (3.0) $32^4 - 1$ Melissa Kuskowski, 5/07 Olathe, KS |
1048576 (3.0) $32^4 \times 1$ Melissa Kuskowski, 5/07 Olathe, KS |
1048577 (3.0) $32^4 + 1$ Melissa Kuskowski, 4/07 Olathe, KS |
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| 1156000 (3.4) $\dfrac{34^2}{.1\%}$ Samantha Maupin, 7/12 Lawrence, KS |
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| 1166886 (3.2) $21^4 \times 3!$ Samantha Maupin, 6/12 Lawrence, KS |
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| 1847042 (3.0) $31^4 \times 2$ Zhenghong To, 5/10 Overland Park, KS |
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| 1906624 (3.0) $124^3$ Megan Cunningham, 9/09 Shawnee, KS |
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| 2985984 (3.4) $(4! \times 3!)^{2+1}$ Rabeh Ghadiri, 12/08 Overland Park, KS |
2985988 (3.2) $12^{3!} + 4$ Matthew Stevens, 5/10 Overland Park, KS |
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| 3111696 (3.0) $42^{3+1}$ Denise Fernandes, 5/10 Lawrence, KS |
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| 3446050 (3.2) $\dfrac{41^3}{2\%}$ Michelle Spencer, 7/11 Harrisonville, MO |
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| 3764768 (3.2) $\dfrac{14^{3!}}{2}$ Dominic Clemente, 6/12 Lawrence, KS |
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| 4782967 (3.0) $3^{14} - 2$ Xinpei Zhao, 6/12 Lawrence, KS |
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| 4782971 (3.0) $3^{14} + 2$ Xinpei Zhao, 6/12 Lawrence, KS |
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| 4826809 (3.0) $13^{4+2}$ Chris Harris, 7/12 Overland Park, KS |
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| 6291456 (3.2) $3 \times \sqrt{4^{21}}$ Michael Freeman, 10/10 Merriam, KS |
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| 6912000 (3.4) $\dfrac{12^4}{.3\%}$ Jordan Pfeiffer, 6/12 Mission Woods, KS |
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| 7408800 (3.2) $\dfrac{42^3}{1\%}$ Michelle Spencer, 7/11 Harrisonville, MO |
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| 7484400 (3.2) $\dfrac{12!}{4^3}$ Larry Flanagan, 7/12 Lawrence, KS |
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| 7962626 (3.4) $4!^{3!-1} + 2$ Tami Lawler-Bontrager, 11/07 Overland Park, KS |
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| 8388608 (3.2) $\sqrt{(4 \times 1)^{23}}$ Tiffany Copple, 2/07 Overland Park, KS |
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| 9565938 (3.0) $2 \times 3^{14}$ Zhedong Liu, 7/12 Lawrence, KS |
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| 9800344 (3.0) $214^3$ Michele Gaston, 12/10 Olathe, KS |
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| 12754584 (3.2) $4! \times 3^{12}$ Zhedong Liu, 7/12 Lawrence, KS |
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| 16777213 (3.2) $2^{4!} - 3 \times 1$ Haoyuan Wu, 6/12 Lawrence, KS |
16777214 (3.2) $2^{4!} - 3 + 1$ Haoyuan Wu, 6/12 Lawrence, KS |
16777218 (3.2) $2^{4!} + 3 - 1$ Haoyuan Wu, 6/12 Lawrence, KS |
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| 25401599 (3.2) $(4 + 3)!^2 - 1$ Eric Anderson, 12/09 Overland Park, KS |
25401600 (3.2) $(4 + 3)!^2 \times 1$ Eric Anderson, 12/09 Overland Park, KS |
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| 25401601 (3.2) $(4 + 3)!^2 + 1$ Eric Anderson, 12/09 Overland Park, KS |
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| 43046721 (3.0) $3^{14 + 2}$ Xinpei Zhao, 6/12 Lawrence, KS |
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| 46176050 (3.2) $\dfrac{31^4}{2\%}$ Michelle Spencer, 7/11 Harrisonville, MO |
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| 67108862 (3.0) $4^{13} - 2$ Xinpei Zhao, 6/12 Lawrence, KS |
67108866 (3.0) $4^{13} + 2$ Xinpei Zhao, 6/12 Lawrence, KS |
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| 69934528 (3.0) $412^3$ Scott Dixon, 9/07 Lenexa, KS |
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| 72681840 (5.2) ${}_{4! - 1} P_{3 \times 2}$ Javier Vizcarra, 7/12 Lawrence, KS |
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| 74618461 (3.0) $421^3$ Melissa Kuskowski, 4/07 Olathe, KS |
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| 74649600 (3.4) $\dfrac{12^{3!}}{4\%}$ Larry Flanagan, 7/12 Lawrence, KS |
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| 85766117 (3.2) $21^{3!} - 4$ Josh Hood, 6/12 Olathe, KS |
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| 85766125 (3.2) $21^{3!} + 4$ Josh Hood, 6/12 Olathe, KS |
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| 119750397 (3.2) $\dfrac{12!}{4} - 3$ Michael Freeman, 11/10 Merriam, KS |
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| 119750403 (3.2) $\dfrac{12!}{4} + 3$ Michael Freeman, 12/10 Merriam, KS |
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| 128024064 (3.2) $(4! \times 21)^3$ Yue Li, 6/12 Lawrence, KS |
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| 159667204 (3.2) $\dfrac{12!}{3} + 4$ Michael Freeman, 12/10 Merriam, KS |
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| 167961600 (3.4) $\dfrac{3!^{4 \times 2}}{1\%}$ Tami Lawler-Bontrager, 11/07 Overland Park, KS |
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| 191102975 (3.6) $4!^{3!} - 1^{2!}$ Rabeh Ghadiri, 11/08 Overland Park, KS |
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| 207359999 (3.2) $(3 + 2)!^4 - 1$ Eric Anderson, 11/09 Overland Park, KS |
207360000 (3.2) $(3 + 2)!^4 \times 1$ Eric Anderson, 11/09 Overland Park, KS |
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| 207360001 (3.2) $(3 + 2)!^4 + 1$ Eric Anderson, 11/09 Overland Park, KS |
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| 228886641 (3.0) $123^4$ Jay Roath, 4/06 Overland Park, KS |
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| 287400960 (3.4) $12! \times 3 \times \sqrt{4}$ Nick Evans, 6/12 Lawrence, KS |
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| 303595776 (3.0) $132^4$ Stacey Henry, 9/10 Overland Park, KS |
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| 359251200 (3.2) $12! \times \dfrac34$ Chelsea Kiddle, 9/12 Leawood, KS |
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| 373247999 (3.2) $(4 + 2)!^3 - 1$ Eric Anderson, 12/09 Overland Park, KS |
373248000 (3.2) $(4 + 2)!^3 \times 1$ Eric Anderson, 11/09 Overland Park, KS |
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| 373248001 (3.2) $(4 + 2)!^3 + 1$ Eric Anderson, 12/09 Overland Park, KS |
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| 479001601 (3.2) $12! + 4 - 3$ Ninglu Ma, 7/12 Lawrence, KS |
479001607 (3.2) $12! + 4 + 3$ Michael Freeman, 11/10 Merriam, KS |
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| 479001630 (3.6) $12! + 4! + 3!$ Michael Freeman, 12/10 Merriam, KS |
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| 479001634 (3.2) $12! + 34$ Yue Li, 6/12 Lawrence, KS |
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| 479001643 (3.2) $12! + 43$ Yue Li, 6/12 Lawrence, KS |
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| 479001681 (3.2) $12! + 3^4$ Josh Hood, 6/12 Olathe, KS |
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| 718502400 (3.4) $12! \times \dfrac{3!}{4}$ Nick Evans, 6/12 Lawrence, KS |
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| 1437004804 (3.2) $12! \times 3 + 4$ Ninglu Ma, 7/12 Lawrence, KS |
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| 2058346161 (3.0) $213^4$ Jay Roath, 4/06 Overland Park, KS |
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| 2375052121 (3.2) $\dfrac{41^{3!}}{2}$ Matthew Stevens, 5/10 Overland Park, KS |
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| 2724321600 (3.2) $\dfrac{14!}{32}$ Michael Freeman, 11/10 Merriam, KS |
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| 2847396321 (3.0) $231^4$ Jay Roath, 4/06 Overland Park, KS |
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| 3113510400 (3.2) $13! \times \dfrac24$ Nick Evans, 6/12 Lawrence, KS |
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| 4294967296 (3.2) $\sqrt{(4 \times 1)^{32}}$ Michael Freeman, 10/10 Merriam, KS |
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| 4750104239 (3.2) $41^{3!} - 2$ Matthew Stevens, 5/10 Overland Park, KS |
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| 4750104243 (3.2) $41^{3!} + 2$ Matthew Stevens, 5/10 Overland Park, KS |
||||||||||
| 5489031743 (3.2) $42^{3!} - 1$ Matthew Stevens, 4/10 Overland Park, KS |
5489031744 (3.2) $42^{3!} \times 1$ Matthew Stevens, 4/10 Overland Park, KS |
5489031745 (3.2) $42^{3!} + 1$ Matthew Stevens, 5/10 Overland Park, KS |
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| 6227020802 (3.2) $13! + 4 - 2$ Ninglu Ma, 7/12 Lawrence, KS |
6227020806 (3.2) $13! + 4 + 2$ Michael Freeman, 11/10 Merriam, KS |
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| 6227020824 (3.2) $13! + 24$ Ninglu Ma, 7/12 Lawrence, KS |
6227020826 (3.4) $13! + 4! + 2$ Michael Freeman, 11/10 Merriam, KS |
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| 6227020842 (3.2) $13! + 42$ Ninglu Ma, 7/12 Lawrence, KS |
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| 9475854336 (3.0) $312^4$ Jay Roath, 4/06 Overland Park, KS |
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| 9500208482 (3.2) $41^{3!} \times 2$ Zhenghong To, 5/10 Overland Park, KS |
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| 10617447681 (3.0) $321^4$ Sarah Brady, 11/10 Vancouver, WA |
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| 17179869183 (3.0) $2^{34} - 1$ Eric Anderson, 9/09 Overland Park, KS |
17179869184 (3.0) $2^{34} \times 1$ Dane Miller, 12/07 Louisburg, KS |
17179869185 (3.0) $2^{34} + 1$ Dane Miller, 12/07 Louisburg, KS |
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| 282429536480 (3.0) $3^{24} - 1$ Eric Anderson, 9/09 Overland Park, KS |
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| 282429536481 (3.0) $3^{24} \times 1$ Dane Miller, 12/07 Louisburg, KS |
282429536482 (3.0) $3^{24} + 1$ Eric Anderson, 9/09 Overland Park, KS |
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| 70368744177663 (3.0) $4^{23} - 1$ Eric Anderson, 9/09 Overland Park, KS |
70368744177664 (3.0) $4^{23} \times 1$ Dane Miller, 12/07 Louisburg, KS |
70368744177665 (3.0) $4^{23} + 1$ Dane Miller, 12/07 Louisburg, KS |
||||||||
| little googol (3.2) $2^{(3+1)/(4\%)}$ Ralph Jeffords, 5/08 Centreville, VA |
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| googol (3.6) $\sqrt[(3-4)\%]{.2-.1}$ Pellegrini Paolo, 8/08 Martina Franca, Italy |
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| googolplex (4.0) $.1^{-\left(\sqrt[-2\%]{(4-3)\%} \right)}$ Pellegrini Paolo, 1/09 Martina Franca, Italy |
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