## Integermania!

#### Largest Four Digits

Using one copy each of the digits 6, 7, 8, and 9, 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), Page 2 (401+).

 401 (3.4) $68 \times (\sqrt{9})! - 7$ Jonathan Frank, 5/21Rye, NY 408 (1.0) $(6 \times 7 + 9) \times 8$ Kenneth Chapman, 10/15Santa Paula, CA 410 (3.4) $67 \times (\sqrt{9})! + 8$ Jonathan Frank, 5/21Rye, NY 415 (3.2) $\sqrt{8^6} - 97$ Emma Perkins, 1/17Wellsville, KS 420 (2.4) $\dfrac{7 \times 6}{.9 - .8}$ Andreina Lugo Parra, 2/15Olathe, KS 425 (1.0) $6 \times 8 \times 9 - 7$ Kenneth Chapman, 9/15Santa Paula, CA 426 (1.0) $(7 \times 9 + 8) \times 6$ Kenneth Chapman, 10/15Santa Paula, CA 432 (3.4) $\dfrac{8!}{7!} \times 9 \times 6$ Carlos Perez, 5/15Overland Park, KS 433 (3.2) $\sqrt{8^6} - 79$ Emma Perkins, 2/17Wellsville, KS 434 (1.0) $(6 \times 9 + 8) \times 7$ Kenneth Chapman, 10/15Santa Paula, CA 439 (1.0) $6 \times 8 \times 9 + 7$ Kenneth Chapman, 9/15Santa Paula, CA 441 (3.4) $\dfrac{9!}{6!} \times \dfrac78$ Jonathan Frank, 5/21Rye, NY 448 (3.4) $\dfrac{9!}{6!} - 8 \times 7$ Jonathan Frank, 5/21Rye, NY 450 (1.0) $(6 \times 7 + 8) \times 9$ Kenneth Chapman, 8/15Santa Paula, CA 456 (1.0) $(7 \times 9 - 6) \times 8$ Kenneth Chapman, 8/15Santa Paula, CA 462 (1.0) $7 \times (8 \times 9 - 6)$ Kenneth Chapman, 9/15Santa Paula, CA 464 (2.0) $(67 - 9) \times 8$ Emma Perkins, 1/17Wellsville, KS 467 (2.0) $68 \times 7 - 9$ Jonathan Frank, 6/21Rye, NY 468 (2.0) $(87 - 9) \times 6$ Emma Perkins, 1/17Wellsville, KS 470 (3.4) $68 \times 7 - (\sqrt{9})!$ Jonathan Frank, 6/21Rye, NY 473 (3.2) $68 \times 7 - \sqrt{9}$ Jonathan Frank, 6/21Rye, NY 474 (1.0) $6 \times (7 + 8 \times 9)$ Kenneth Chapman, 9/15Santa Paula, CA 477 (2.0) $6 \times 78 + 9$ Carlos Perez, 3/15Overland Park, KS 479 (3.2) $68 \times 7 + \sqrt{9}$ Jonathan Frank, 6/21Rye, NY 482 (3.4) $68 \times 7 + (\sqrt{9})!$ Jonathan Frank, 6/21Rye, NY 485 (2.0) $68 \times 7 + 9$ Carlos Perez, 3/15Overland Park, KS 488 (1.0) $(6 \times 9 + 7) \times 8$ Kenneth Chapman, 10/15Santa Paula, CA 489 (3.4) $\dfrac{9!}{6!} - 8 - 7$ Jonathan Frank, 4/21Rye, NY 491 (2.0) $69 \times 7 + 8$ Carlos Perez, 3/15Overland Park, KS 492 (2.0) $(89 - 7) \times 6$ Emma Perkins, 1/17Wellsville, KS 495 (1.0) $(6 \times 8 + 7) \times 9$ Kenneth Chapman, 10/15Santa Paula, CA 496 (3.2) $\sqrt{8^6} - 9 - 7$ Emma Perkins, 4/16Wellsville, KS 498 (1.0) $9 \times 8 \times 7 - 6$ Nicole Maberry, 5/15Lawrence, KS 503 (3.4) $\dfrac{9!}{6!} - 8 + 7$ Jonathan Frank, 4/21Rye, NY 504 (3.4) $\dfrac{9!}{6!} \times (8 - 7)$ Jonathan Frank, 4/21Rye, NY 505 (3.4) $\dfrac{9!}{6!} + 8 - 7$ Jonathan Frank, 4/21Rye, NY 510 (1.0) $9 \times 8 \times 7 + 6$ Jaspreet Kaur, 5/15Lenexa, KS 514 (3.2) $\sqrt{8^6} + 9 - 7$ Emma Perkins, 4/16Wellsville, KS 516 (2.2) $\dfrac{7 \times 6}{8\%} - 9$ Yi Zheng, 1/16Olathe, KS 519 (3.4) $\dfrac{9!}{6!} + 8 + 7$ Jonathan Frank, 4/21Rye, NY 522 (2.0) $6 \times (78 + 9)$ Kenneth Chapman, 2/16Santa Paula, CA 525 (3.2) $87 \times 6 + \sqrt{9}$ Steven Clifford, 2/17Mission, KS 527 (2.0) $89 \times 6 - 7$ Darien Chambers, 6/15Ottawa, KS 528 (3.2) $\sqrt{8^6} + 9 + 7$ Emma Perkins, 4/16Wellsville, KS 531 (2.0) $(67 - 8) \times 9$ Emma Perkins, 1/17Wellsville, KS 534 (2.2) $\dfrac{7 \times 6}{8\%} + 9$ Yi Zheng, 1/16Olathe, KS 536 (2.0) $8 \times (76 - 9)$ Kenneth Chapman, 2/16Santa Paula, CA 539 (2.0) $7 \times (86 - 9)$ Kenneth Chapman, 2/16Santa Paula, CA 546 (1.0) $(9 \times 8 + 6) \times 7$ Alex Hwang, 4/15Overland Park, KS 552 (1.0) $(7 \times 9 + 6) \times 8$ Steve Wilson, 8/15Lawrence, KS 558 (1.0) $(6 + 7 \times 8) \times 9$ Kenneth Chapman, 11/15Santa Paula, CA 559 (2.0) $69 \times 8 + 7$ Emma Perkins, 2/16Wellsville, KS 574 (3.2) $\dfrac{7!}{9} + 6 + 8$ Nicole Maberry, 5/15Lawrence, KS 575 (3.2) $\sqrt{8^6} + 7 \times 9$ Jake Karst, 5/17Overland Park, KS 576 (2.0) $(89 + 7) \times 6$ Jessica Hodge, 5/16Overland Park, KS 580 (2.2) $8.7 \times \dfrac{6}{9\%}$ Steve Wilson, 8/15Lawrence, KS 581 (2.0) $6 \times 98 - 7$ Javion Grant, 7/14Kansas City, KS 591 (3.2) $\sqrt{8^6} + 79$ Emma Perkins, 4/16Wellsville, KS 595 (2.0) $98 \times 6 + 7$ Alondra Aviles Gallegos, 3/17Kansas City, KS 596 (5.0) ${}_9 C_6 \times 7 + 8$ Andreina Lugo Parra, 5/15Olathe, KS 599 (2.0) $76 \times 8 - 9$ Brittany Potter, 8/15Olathe, KS 608 (2.0) $(69 + 7) \times 8$ Callie Biddle, 5/16Olathe, KS 609 (3.2) $\sqrt{8^6} + 97$ Emma Perkins, 4/16Wellsville, KS 616 (2.0) $(96 - 8) \times 7$ Emma Perkins, 1/16Wellsville, KS 617 (2.0) $89 \times 7 - 6$ Emma Perkins, 2/16Wellsville, KS 619 (2.0) $68 \times 9 + 7$ Alondra Aviles Gallegos, 3/17Kansas City, KS 629 (2.0) $89 \times 7 + 6$ Emma Perkins, 2/16Wellsville, KS 630 (2.0) $(98 + 7) \times 6$ Callie Biddle, 5/16Olathe, KS 633 (3.2) $\dfrac{6!}{9} \times 8 - 7$ Nicole Maberry, 5/15Lawrence, KS 638 (2.0) $79 \times 8 + 6$ Callie Biddle, 5/16Olathe, KS 640 (2.2) $\dfrac{96}{(8 + 7)\%}$ Kacie Strouse, 1/17Blue Springs, MO 642 (3.2) $\sqrt{9^6} - 87$ Emma Perkins, 2/17Wellsville, KS 644 (2.0) $(98 - 6) \times 7$ Alex Hwang, 3/15Overland Park, KS 651 (3.2) $\sqrt{9^6} - 78$ Susan Vongphrachanh, 2/17Kansas City, KS 664 (2.0) $96 \times 7 - 8$ Susan Vongphrachanh, 2/17Kansas City, KS 665 (2.0) $(89 + 6) \times 7$ Jessica Hodge, 4/16Overland Park, KS 669 (2.0) $678 - 9$ Kacie Strouse, 1/17Blue Springs, MO 675 (2.0) $(67 + 8) \times 9$ Callie Biddle, 5/16Olathe, KS 678 (2.0) $687 - 9$ Susan Vongphrachanh, 2/17Kansas City, KS 680 (2.0) $96 \times 7 + 8$ Alex Hwang, 5/15Overland Park, KS 682 (2.2) $\dfrac{9 \times 6}{8\%} + 7$ Yi Zheng, 1/16Olathe, KS 692 (2.0) $98 \times 7 + 6$ Emma Perkins, 2/16Wellsville, KS 696 (2.0) $78 \times 9 - 6$ Alex Hwang, 4/15Overland Park, KS 705 (2.0) $698 + 7$ Jessica Hodge, 4/16Overland Park, KS 708 (2.0) $78 \times 9 + 6$ Emma Perkins, 2/16Wellsville, KS 712 (2.0) $(96 - 7) \times 8$ Alex Hwang, 4/15Overland Park, KS 714 (1.0) $7 \times 6 \times (9 + 8)$ Javion Grant, 7/14Kansas City, KS 720 (2.4) $\dfrac{9 \times 8}{.7 - .6}$ Andreina Lugo Parra, 3/15Olathe, KS 728 (3.2) $\sqrt{9^6} - 8 + 7$ Emma Perkins, 3/16Wellsville, KS 730 (3.2) $\sqrt{9^6} + 8 - 7$ Emma Perkins, 3/16Wellsville, KS 744 (3.2) $\sqrt{9^6} + 8 + 7$ Emma Perkins, 3/16Wellsville, KS 756 (2.0) $(78 + 6) \times 9$ Jessica Hodge, 4/16Overland Park, KS 767 (2.0) $86 \times 9 - 7$ Alex Hwang, 4/15Overland Park, KS 768 (1.0) $8 \times 6 \times (9 + 7)$ Alex Hwang, 2/15Overland Park, KS 770 (2.0) $97 \times 8 - 6$ Alex Hwang, 5/15Overland Park, KS 777 (2.0) $786 - 9$ Kacie Strouse, 1/17Blue Springs, MO 781 (2.0) $86 \times 9 + 7$ Callie Biddle, 5/16Olathe, KS 795 (2.0) $789 + 6$ Jessica Hodge, 5/16Overland Park, KS 799 (3.2) $6! + 7 + 8 \times 9$ Carlos Perez, 4/15Overland Park, KS 807 (3.2) $\sqrt{9^6} + 78$ Emma Perkins, 3/16Wellsville, KS 810 (1.0) $9 \times 6 \times (8 + 7)$ Alex Hwang, 2/15Overland Park, KS 816 (3.2) $\sqrt{9^6} + 87$ Emma Perkins, 3/16Wellsville, KS 824 (2.0) $(96 + 7) \times 8$ Alex Hwang, 3/15Overland Park, KS 837 (2.0) $(86 + 7) \times 9$ Jessica Hodge, 4/16Overland Park, KS 840 (1.0) $7 \times 8 \times (6 + 9)$ Kenneth Chapman, 11/15Santa Paula, CA 858 (2.0) $867 - 9$ Lawrence Ombasa, 4/16Overland Park, KS 879 (3.2) $876 + \sqrt{9}$ Salvador Aguirre, 9/16Overland Park, KS 882 (1.0) $7 \times 9 \times (6 + 8)$ Kenneth Chapman, 11/15Santa Paula, CA 903 (2.0) $896 + 7$ Jessica Hodge, 5/16Overland Park, KS 929 (3.2) $\dfrac{7!}{6} + 89$ Jon Alan Rubendall, 4/17Lansing, KS 936 (1.0) $9 \times 8 \times (7 + 6)$ Alex Hwang, 2/15Overland Park, KS 972 (2.0) $978 - 6$ Alondra Aviles Gallegos, 2/17Kansas City, KS 979 (2.0) $986 - 7$ Kacie Strouse, 1/17Blue Springs, MO 980 (2.4) $\dfrac{98}{.7 - .6}$ Andreina Lugo Parra, 3/15Olathe, KS 981 (2.0) $987 - 6$ Alex Hwang, 1/15Overland Park, KS 984 (2.0) $978 + 6$ Jessica Hodge, 4/16Overland Park, KS 993 (2.0) $987 + 6$ Jessica Hodge, 5/16Overland Park, KS 1008 (3.2) $6 \times 7 \times 8 \times \sqrt{9}$ Emma Perkins, 1/16Wellsville, KS 1024 (3.2) $\left( \dfrac{6}{\sqrt{9}} \right)^7 \times 8$ Susan Vongphrachanh, 2/17Kansas City, KS 1035 (2.0) $69 \times (7 + 8)$ Lawrence Ombasa, 1/16Overland Park, KS 1157 (2.0) $(6 + 7) \times 89$ Jon Alan Rubendall, 4/17Lansing, KS 1170 (2.2) $78 \times \dfrac{9}{.6}$ Jon Rubendall, 3/17Lansing, KS 1193 (2.2) $\dfrac{9 \times 8}{6\%} - 7$ Yi Zheng, 1/16Olathe, KS 1199 (3.2) $\sqrt{6^8} - 97$ Emma Perkins, 2/17Wellsville, KS 1207 (2.2) $\dfrac{9 \times 8}{6\%} + 7$ Yi Zheng, 1/16Olathe, KS 1217 (3.2) $\sqrt{6^8} - 79$ Emma Perkins, 2/17Wellsville, KS 1224 (3.2) $6! + 7 \times 8 \times 9$ Carlos Perez, 4/15Overland Park, KS 1274 (2.0) $(6 + 7) \times 98$ Jon Alan Rubendall, 4/17Lansing, KS 1291 (2.2) $\dfrac{78}{6\%} - 9$ Kacie Strouse, 1/17Blue Springs, MO 1393 (3.2) $\sqrt{6^8} + 97$ Emma Perkins, 2/17Wellsville, KS 1428 (3.2) $68 \times 7 \times \sqrt{9}$ Stephanie Cantrell, 4/16Louisburg, KS 1440 (2.0) $(7 + 8) \times 96$ Jon Rubendall, 3/17Lansing, KS 1608 (3.2) $67 \times 8 \times \sqrt{9}$ Stephanie Cantrell, 4/16Louisburg, KS 2034 (3.2) $678 \times \sqrt{9}$ Jon Rubendall, 3/17Lansing, KS 2304 (3.2) $768 \times \sqrt{9}$ Jon Rubendall, 3/17Lansing, KS 2601 (3.2) $867 \times \sqrt{9}$ Steven Clifford, 5/17Mission, KS 3024 (1.0) $9 \times 8 \times 7 \times 6$ Andreina Lugo Parra, 1/15Olathe, KS 3738 (2.0) $89 \times 7 \times 6$ Stephanie Cantrell, 3/16Louisburg, KS 3888 (3.0) $\dfrac{6^7}{8 \times 9}$ Emma Perkins, 1/16Wellsville, KS 4116 (2.0) $6 \times 7 \times 98$ Alex Hwang, 5/15Overland Park, KS 4424 (3.4) $\dfrac{8!}{6!} \times 79$ Jon Alan Rubendall, 4/17Lansing, KS 4698 (2.0) $87 \times 9 \times 6$ Alex Hwang, 5/15Overland Park, KS 4734 (2.0) $789 \times 6$ Jessica Hodge, 5/16Overland Park, KS 4824 (2.0) $67 \times 8 \times 9$ Alex Hwang, 5/15Overland Park, KS 4886 (2.0) $698 \times 7$ Stephanie Cantrell, 3/16Louisburg, KS 5057 (3.2) $6! \times 7 + 8 + 9$ Jaspreet Kaur, 4/15Lenexa, KS 5274 (2.0) $879 \times 6$ Alondra Aviles Gallegos, 2/17Kansas City, KS 5372 (2.0) $68 \times 79$ Callie Biddle, 3/16Olathe, KS 5376 (2.0) $96 \times 8 \times 7$ Alex Hwang, 3/15Overland Park, KS 5382 (2.0) $78 \times 69$ Nicole Maberry, 5/15Lawrence, KS 5432 (2.0) $679 \times 8$ Carlos Perez, 3/15Overland Park, KS 5670 (3.2) $6! \times 7 \times \dfrac98$ Carlos Perez, 5/15Overland Park, KS 5758 (3.2) $6! \times 8 - 9 + 7$ Parker Thomsen, 4/15Lenexa, KS 5776 (3.2) $6! \times 8 + 9 + 7$ Parker Thomsen, 4/15Lenexa, KS 5868 (2.0) $978 \times 6$ Callie Biddle, 2/16Olathe, KS 5922 (2.0) $987 \times 6$ Callie Biddle, 2/16Olathe, KS 5963 (2.0) $67 \times 89$ Callie Biddle, 3/16Olathe, KS 6003 (2.0) $69 \times 87$ Callie Biddle, 3/16Olathe, KS 6102 (2.0) $678 \times 9$ Callie Biddle, 2/16Olathe, KS 6368 (2.0) $796 \times 8$ Stephanie Cantrell, 4/16Louisburg, KS 6566 (2.0) $98 \times 67$ Javion Grant, 7/14Kansas City, KS 6711 (3.2) $7! \times \dfrac86 - 9$ Parker Thomsen, 4/15Lenexa, KS 6729 (3.2) $7! \times \dfrac86 + 9$ Parker Thomsen, 4/15Lenexa, KS 6736 (3.2) $\dfrac{8!}{6} + 9 + 7$ Carlos Perez, 4/15Overland Park, KS 6764 (2.0) $76 \times 89$ Callie Biddle, 3/16Olathe, KS 6776 (2.0) $968 \times 7$ Alex Hwang, 1/15Overland Park, KS 6783 (3.2) $\dfrac{8!}{6} + 9 \times 7$ Carlos Perez, 4/15Overland Park, KS 6789 (2.0) $6789$ Bruno Biazetto, 2/17Overland Park, KS 6794 (2.0) $79 \times 86$ Jaspreet Kaur, 5/15Lenexa, KS 6798 (2.0) $6798$ Bruno Biazetto, 5/17Overland Park, KS 6902 (2.0) $986 \times 7$ Kashmira Sayani, 1/17Overland Park, KS 6987 (2.0) $6987$ Bruno Biazetto, 3/17Overland Park, KS 7110 (3.2) $79 \times \dfrac{6!}{8}$ Jon Alan Rubendall, 4/17Lansing, KS 7448 (2.0) $98 \times 76$ Andreina Lugo Parra, 1/15Olathe, KS 7488 (2.0) $96 \times 78$ Alex Hwang, 1/15Overland Park, KS 7552 (3.2) $7! \times \dfrac96 - 8$ Parker Thomsen, 4/15Lenexa, KS 7689 (2.0) $7689$ Bruno Biazetto, 2/17Overland Park, KS 7698 (2.0) $7698$ Bruno Biazetto, 2/17Overland Park, KS 7736 (2.0) $967 \times 8$ Callie Biddle, 2/16Olathe, KS 7808 (2.0) $976 \times 8$ Callie Biddle, 2/16Olathe, KS 7869 (2.0) $7869$ Bruno Biazetto, 3/17Overland Park, KS 7884 (2.0) $9 \times 876$ Javion Grant, 7/14Kansas City, KS 7896 (2.0) $7896$ Bruno Biazetto, 3/17Overland Park, KS 7986 (2.0) $7986$ Bruno Biazetto, 5/17Overland Park, KS 8342 (2.0) $97 \times 86$ Emma Perkins, 1/16Wellsville, KS 8352 (2.0) $96 \times 87$ Callie Biddle, 3/16Olathe, KS 8400 (2.2) $96 \times \dfrac{7}{8\%}$ Connor Perrine, 5/15Olathe, KS 8679 (2.0) $8679$ Bruno Biazetto, 5/17Overland Park, KS 8769 (2.0) $8769$ Bruno Biazetto, 2/17Overland Park, KS 8967 (2.0) $8967$ Bruno Biazetto, 3/17Overland Park, KS 8976 (2.0) $8976$ Bruno Biazetto, 3/17Overland Park, KS 9600 (3.4) $\dfrac{8! + 9!}{6 \times 7}$ Jaspreet Kaur, 5/15Lenexa, KS 9867 (2.0) $9867$ Bruno Biazetto, 5/17Overland Park, KS 9876 (2.0) $9876$ Bruno Biazetto, 2/17Overland Park, KS 11700 (2.2) $78 \times \dfrac{9}{6\%}$ Connor Perrine, 5/15Olathe, KS 13050 (2.2) $87 \times \dfrac{9}{6\%}$ Connor Perrine, 5/15Olathe, KS 30257 (3.2) $7! \times 6 + 8 + 9$ Jaspreet Kaur, 4/15Lenexa, KS 30527 (3.2) $89 \times \sqrt{7^6}$ Steven Clifford, 2/17Mission, KS 33614 (3.2) $98 \times \sqrt{7^6}$ Steven Clifford, 5/17Mission, KS 34020 (3.2) $7! \times 6 \times \dfrac98$ Connor Perrine, 4/15Olathe, KS 34983 (3.0) $\dfrac{6^7}{8} - 9$ Jared Anderson, 12/16Olathe, KS 35001 (3.0) $\dfrac{6^7}{8} + 9$ Jared Anderson, 12/16Olathe, KS 40448 (3.2) $79 \times \sqrt{8^6}$ Steven Clifford, 2/17Mission, KS 49664 (3.2) $97 \times \sqrt{8^6}$ Steven Clifford, 5/17Mission, KS 50400 (3.4) $\dfrac{6! \times 7!}{8 \times 9}$ Jaspreet Kaur, 5/15Lenexa, KS 56862 (3.2) $78 \times \sqrt{9^6}$ Steven Clifford, 3/17Mission, KS 60480 (3.2) $7! \times 8 \times \dfrac96$ Hunter Harlow, 4/15Lenexa, KS 63423 (3.2) $87 \times \sqrt{9^6}$ Steven Clifford, 2/17Mission, KS 68040 (3.6) $\dfrac{9! + 8! + 7!}{6}$ Tanner Schremmer, 4/16Olathe, KS 102384 (3.2) $79 \times \sqrt{6^8}$ Steven Clifford, 2/17Mission, KS 117649 (3.0) $(9 - 8) \times 7^6$ Hamza Damer, 4/17Lenexa, KS 117721 (3.0) $7^6 + 8 \times 9$ Chryspus Muema, 2/16Olathe, KS 117738 (3.0) $7^6 + 89$ Andy Cauthon, 5/17Shawnee, KS 125712 (3.2) $97 \times \sqrt{6^8}$ Steven Clifford, 5/17Mission, KS 148716 (3.2) $68 \times \sqrt{9^7}$ Steven Clifford, 4/17Mission, KS 165669 (3.2) $69 \times \sqrt{7^8}$ Steven Clifford, 4/17Mission, KS 188082 (3.2) $86 \times \sqrt{9^7}$ Steven Clifford, 4/17Mission, KS 230496 (3.2) $96 \times \sqrt{7^8}$ Steven Clifford, 2/17Mission, KS 241936 (3.2) $8! \times 6 + 7 + 9$ Jaspreet Kaur, 4/15Lenexa, KS 248832 (3.0) $6^7 \times \dfrac{8}{9}$ Morgan Sievert, 4/17Olathe, KS 262065 (3.0) $8^6 - 79$ Stephanie Cantrell, 4/16Louisburg, KS 262146 (3.0) $8^6 + 9 - 7$ Steven Clifford, 3/17Mission, KS 279838 (3.0) $6^7 - 98$ Andy Cauthon, 5/17Shawnee, KS 311040 (3.2) $8! \times 9 \times \dfrac67$ Carlos Perez, 5/15Overland Park, KS 314928 (3.0) $6^7 \times \dfrac{9}{8}$ Morgan Sievert, 4/17Olathe, KS 318240 (3.8) $9! - 8! - 7! + 6!$ Tanner Schremmer, 4/16Olathe, KS 326880 (3.8) $9! - 8! + 7! - 6!$ Tanner Schremmer, 4/16Olathe, KS 362145 (3.4) $9! - 6! - 8 - 7$ Waleed Saifan, 4/16Lenexa, KS 362880 (3.2) $6! \times 7 \times 8 \times 9$ Jaspreet Kaur, 3/15Lenexa, KS 363585 (3.4) $9! + 6! - 8 - 7$ Waleed Saifan, 4/16Lenexa, KS 363599 (3.4) $9! + 6! - 8 + 7$ Waleed Saifan, 4/16Lenexa, KS 363601 (3.4) $9! + 6! + 8 - 7$ Waleed Saifan, 4/16Lenexa, KS 367934 (3.4) $9! + 7! + 8 + 6$ Jaspreet Kaur, 3/15Lenexa, KS 397440 (3.8) $9! + 8! - 7! - 6!$ Tanner Schremmer, 4/16Olathe, KS 407520 (3.8) $9! + 8! + 7! - 6!$ Tanner Schremmer, 4/16Olathe, KS 531442 (3.0) $9^6 + 8 - 7$ Steven Clifford, 3/17Mission, KS 531497 (3.0) $9^6 + 8 \times 7$ Chryspus Muema, 2/16Olathe, KS 941183 (3.0) $7^6 \times 8 - 9$ Morgan Sievert, 5/17Olathe, KS 1058833 (3.0) $9 \times 7^6 - 8$ Andrea Craig, 4/17Olathe, KS 1259719 (3.0) $\dfrac{6^9}{8} + 7$ Stephanie Cantrell, 3/16Louisburg, KS 1684647 (3.2) $7! + 6^8 - 9$ Adam Shafton, 2/16Overland Park, KS 1684665 (3.2) $7! + 6^8 + 9$ Adam Shafton, 2/16Overland Park, KS 2000033 (3.0) $(8 + 9) \times 7^6$ Hamza Damer, 4/17Lenexa, KS 2097137 (3.0) $8^7 - 9 - 6$ Andy Cauthon, 5/17Shawnee, KS 2097155 (3.0) $8^7 + 9 - 6$ Steven Clifford, 3/17Mission, KS 2177295 (3.2) $9! \times 6 + 7 + 8$ Jaspreet Kaur, 4/15Lenexa, KS 2239479 (3.0) $6^7 \times 8 - 9$ Morgan Sievert, 4/17Olathe, KS 2359289 (3.0) $8^6 \times 9 - 7$ Jared Anderson, 12/16Olathe, KS 2519416 (3.0) $6^7 \times 9 - 8$ Morgan Sievert, 4/17Olathe, KS 2628593 (3.0) $9^6 + 8^7$ Trevor Brock, 4/17Olathe, KS 2903053 (3.2) $9! \times 8 + 7 + 6$ Jaspreet Kaur, 3/15Lenexa, KS 3229632 (3.6) $6! \times 7! \times 89\%$ Connor Perrine, 4/15Olathe, KS 3556224 (3.6) $6! \times 7! \times 98\%$ Connor Perrine, 4/15Olathe, KS 4082400 (3.4) $6! \times 7! \times \dfrac98$ Carlos Perez, 5/15Overland Park, KS 4251535 (3.0) $9^6 \times 8 + 7$ Obada Albadawi, 2/16Overland Park, KS 4312895 (3.0) $6^9 - 7^8$ Chryspus Muema, 2/16Olathe, KS 4347000 (3.4) $69 \times \dfrac{7!}{8\%}$ Connor Perrine, 5/15Olathe, KS 4717440 (3.2) $78 \times \dfrac{9!}{6}$ Connor Perrine, 5/15Olathe, KS 4758912 (3.0) $(8 + 9) \times 6^7$ Hamza Damer, 4/17Lenexa, KS 4782883 (3.0) $9^7 - 86$ Jake Karst, 5/17Overland Park, KS 4782921 (3.0) $9^7 - 6 \times 8$ Stephanie Cantrell, 4/16Louisburg, KS 5045113 (3.0) $9^7 + 8^6$ Stephanie Cantrell, 3/16Louisburg, KS 8470728 (3.0) $7^6 \times 8 \times 9$ Morgan Sievert, 5/17Olathe, KS 10077697 (3.0) $6^9 + 8 - 7$ Jake Karst, 5/17Overland Park, KS 10082728 (3.2) $7! + 6^9 - 8$ Adam Shafton, 2/16Overland Park, KS 10082744 (3.2) $7! + 6^9 + 8$ Adam Shafton, 2/16Overland Park, KS 11757303 (3.0) $6^8 \times 7 - 9$ Morgan Sievert, 5/17Olathe, KS 11757321 (3.0) $6^8 \times 7 + 9$ Morgan Sievert, 5/17Olathe, KS 12174848 (3.0) $6^9 + 8^7$ Stephanie Cantrell, 3/16Louisburg, KS 15116537 (3.0) $9 \times 6^8 - 7$ Andrea Craig, 4/17Olathe, KS 15240968 (3.2) $9! \times 6 \times 7 + 8$ Jaspreet Kaur, 4/15Lenexa, KS 15842497 (3.0) $6^9 + 7^8$ Chryspus Muema, 2/16Olathe, KS 16515072 (3.0) $8^6 \times 7 \times 9$ Obada Albadawi, 2/16Overland Park, KS 20155392 (3.0) $6^7 \times 8 \times 9$ Morgan Sievert, 4/17Olathe, KS 28667520 (3.6) $6! \times 7! \times 8 - 9!$ Waleed Saifan, 4/16Lenexa, KS 38263746 (3.0) $8 \times 9^7 - 6$ Andrea Craig, 4/17Olathe, KS 38263758 (3.0) $8 \times 9^7 + 6$ Andrea Craig, 4/17Olathe, KS 38673991 (3.0) $7^9 - 6^8$ Salvador Aguirre, 9/16Overland Park, KS 40091463 (3.0) $7^9 - 8^6$ Salvador Aguirre, 9/16Overland Park, KS 40615751 (3.0) $8^6 + 7^9$ Andy Cauthon, 5/17Shawnee, KS 42766785 (3.0) $9^8 - 6^7$ Chryspus Muema, 2/16Olathe, KS 42929072 (3.0) $9^8 - 7^6$ Andy Cauthon, 5/17Shawnee, KS 43046721 (3.0) $(7 - 6) \times 9^8$ Obada Albadawi, 2/16Overland Park, KS 43326657 (3.0) $9^8 + 6^7$ Steven Clifford, 1/17Mission, KS 51883203 (3.0) $9 \times 7^8 - 6$ Andrea Craig, 4/17Olathe, KS 51883155 (3.0) $(7^8 - 6) \times 9$ Jake Karst, 5/17Overland Park, KS 80626608 (3.2) $7! + 6^9 \times 8$ Adam Shafton, 2/16Overland Park, KS 105815808 (3.0) $6^8 \times 7 \times 9$ Morgan Sievert, 5/17Olathe, KS 134100079 (3.0) $8^9 - 7^6$ Salvador Aguirre, 9/16Overland Park, KS 134217727 (3.0) $8^9 + 6 - 7$ Steven Clifford, 3/17Mission, KS 134217728 (3.0) $(7 - 6) \times 8^9$ Hamza Damer, 4/17Lenexa, KS 134335377 (3.0) $7^6 + 8^9$ Steven Clifford, 1/17Mission, KS 261273600 (3.4) $6! \times 7! \times 8 \times 9$ Jaspreet Kaur, 3/15Lenexa, KS 311299254 (3.0) $7^8 \times 9 \times 6$ Obada Albadawi, 2/16Overland Park, KS 322828850 (3.0) $7^9 \times 8 - 6$ Obada Albadawi, 2/16Overland Park, KS 322828862 (3.0) $7^9 \times 8 + 6$ Salvador Aguirre, 9/16Overland Park, KS 939524090 (3.0) $8^9 \times 7 - 6$ Jared Anderson, 12/16Olathe, KS 939524102 (3.0) $8^9 \times 7 + 6$ Jared Anderson, 12/16Olathe, KS 1219276809 (3.4) $6 \times 7! \times 8! + 9$ Jaspreet Kaur, 3/15Lenexa, KS 1243662336 (3.6) $9! \times 7! \times 68\%$ Connor Perrine, 4/15Olathe, KS 1371686400 (3.4) $7! \times 9! \times \dfrac68$ Carlos Perez, 5/15Overland Park, KS 1572867072 (3.6) $9! \times 7! \times 86\%$ Connor Perrine, 4/15Olathe, KS 1744830464 (3.0) $(6 + 7) \times 8^9$ Hamza Damer, 4/17Lenexa, KS 1807962282 (3.0) $6 \times 7 \times 9^8$ Jake Karst, 5/17Overland Park, KS 3470410202 (3.0) $86 \times 7^9$ Steven Clifford, 5/17Mission, KS

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