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The first four composite numbers are 4, 6, 8, and 9. 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+).
| 1201 (2.6) $8 \times \dfrac{6}{4\%} + .\overline{9}$ Paolo Pellegrini, 6/10 Martina Franca, Italy |
1202 (2.8) $(6 + .\overline{9}\%) \times \dfrac{8}{4\%}$ Paolo Pellegrini, 6/10 Martina Franca, Italy |
1203 (2.8) $\dfrac{8 - 4\%}{.\overline{6}\%} + 9$ Paolo Pellegrini, 6/10 Martina Franca, Italy |
1204 (2.2) $\dfrac{96}{8\%} + 4$ Paolo Pellegrini, 6/10 Martina Franca, Italy |
1205 (2.2) $\dfrac{964}{.8}$ Paolo Pellegrini, 6/10 Martina Franca, Italy |
1206 (2.4) $(8 + 4\%) \times \dfrac{9}{6\%}$ Paolo Pellegrini, 6/10 Martina Franca, Italy |
1207 (2.8) $\dfrac{6}{.\overline{4}\%} \times .9 - 8$ Paolo Pellegrini, 6/10 Martina Franca, Italy |
1208 (2.6) $\dfrac{6}{.4\overline{9}\%} + 8$ Paolo Pellegrini, 6/10 Martina Franca, Italy |
1209 (2.2) $8 \times \dfrac{6}{4\%} + 9$ Paolo Pellegrini, 6/10 Martina Franca, Italy |
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| 1224 (3.0) $6^4 - 9 \times 8$ Zach Burger, 4/05 Overland Park, KS |
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| 1279 (3.0) $6^4 - 9 - 8$ Eric Millard, 5/07 Olathe, KS |
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| 1295 (3.0) $6^4 + 8 - 9$ Ross Andring, 11/06 Osawatomie, KS |
1297 (3.0) $6^4 + 9 - 8$ Cameron Haines, 4/06 Olathe, KS |
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| 1313 (3.0) $6^4 + 8 + 9$ Kimberly Grosdidier, 10/05 Eudora, KS |
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| 1385 (3.0) $6^4 + 89$ Tricia Mahaney, 5/06 Shawnee, KS |
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| 1396 (3.2) $698 \times \sqrt{4}$ Christina Ha, 2/06 Shawnee, KS |
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| 1404 (3.2) $468 \times \sqrt{9}$ Christina Ha, 2/06 Shawnee, KS |
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| 1530 (2.2) $68 \times \dfrac{9}{.4}$ David Mullins, 10/06 Overland Park, KS |
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| 1623 (3.2) $4! \times 68 - 9$ Tina Redlinger, 12/07 Olathe, KS |
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| 1648 (3.2) $4! \times 69 - 8$ Tina Redlinger, 12/07 Olathe, KS |
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| 1728 (1.0) $4 \times 6 \times 8 \times 9$ Adam Petrowsky, 4/03 Lenexa, KS |
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| 1944 (3.2) $648 \times \sqrt{9}$ Cara Seats, 10/07 Lawrence, KS |
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| 2008 (3.4) $\dfrac{9!}{6!} \times 4 - 8$ Harman Tiwana, 10/12 Lenexa, KS |
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| 2024 (3.4) $\dfrac{9!}{6!} \times 4 + 8$ Harman Tiwana, 10/12 Lenexa, KS |
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| 2052 (3.2) $684 \times \sqrt{9}$ Cara Seats, 10/07 Lawrence, KS |
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| 2136 (2.0) $89 \times 6 \times 4$ Alondra Aviles Gallegos, 4/17 Kansas City, KS |
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| 2352 (2.0) $98 \times 4 \times 6$ Tricia Mahaney, 5/06 Shawnee, KS |
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| 2448 (2.0) $68 \times 4 \times 9$ Melody Tarbox, 3/07 Ottawa, KS |
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| 2465 (2.2) $\dfrac{986}{.4}$ Eric Millard, 5/07 Olathe, KS |
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| 2756 (2.0) $689 \times 4$ Bryce Torres, 9/06 Perryton, TX |
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| 2792 (2.0) $698 \times 4$ Bryce Torres, 12/06 Perryton, TX |
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| 2934 (2.0) $489 \times 6$ Bryce Torres, 12/06 Perryton, TX |
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| 2988 (2.0) $498 \times 6$ Bryce Torres, 12/06 Perryton, TX |
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| 3072 (3.0) $6 \times \left( \dfrac84 \right)^9$ Zach Alholm, 10/06 Leawood, KS |
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| 3096 (2.0) $86 \times 9 \times 4$ Tricia Mahaney, 5/06 Shawnee, KS |
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| 3240 (3.2) $\dfrac48 \times 6! \times 9$ Silvana Palau-Valiente, 3/12 Gardner, KS |
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| 3312 (2.0) $48 \times 69$ Ashley Woodward, 1/05 Lawrence, KS |
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| 3332 (2.0) $68 \times 49$ Cara Seats, 9/07 Lawrence, KS |
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| 3476 (2.0) $869 \times 4$ Katie Ware, 1/07 Overland Park, KS |
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| 3584 (2.0) $896 \times 4$ Brittany Borghesi, 11/06 Olathe, KS |
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| 3840 (3.2) $\dfrac{6!}{9} \times 48$ Tina Redlinger, 12/07 Olathe, KS |
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| 3872 (2.0) $968 \times 4$ Shawn Graf, 10/06 Overland Park, KS |
3880 (3.2) $8^4 - 6^{\sqrt{9}}$ Anthony Sands, 3/06 Raytown, MO |
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| 3944 (2.0) $986 \times 4$ Bryce Torres, 9/06 Perryton, TX |
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| 3968 (2.0) $496 \times 8$ Bryce Torres, 12/06 Perryton, TX |
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| 3998 (3.0) $4^6 - 98$ Rabeh Ghadiri, 8/08 Overland Park, KS |
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| 4007 (3.0) $4^6 - 89$ Ross Andring, 11/06 Osawatomie, KS |
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| 4027 (3.0) $8^4 - 69$ Christina Ha, 2/06 Shawnee, KS |
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| 4093 (3.0) $8^4 + 6 - 9$ Tiffany Copple, 1/07 Overland Park, KS |
4094 (2.0) $46 \times 89$ Tim Murphy, 5/03 Olathe, KS |
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| 4111 (3.0) $8^4 + 6 + 9$ Cameron Haines, 5/06 Olathe, KS |
4113 (3.0) $4^6 + 8 + 9$ Tiffany Copple, 1/07 Overland Park, KS |
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| 4168 (3.0) $4^6 + 8 \times 9$ Renato Bacco, 10/07 Overland Park, KS |
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| 4212 (2.0) $468 \times 9$ Katie Ware, 1/07 Overland Park, KS |
4214 (2.0) $49 \times 86$ Steve Wilson, 9/07 Raytown, MO |
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| 4374 (2.0) $486 \times 9$ Katie Ware, 1/07 Overland Park, KS |
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| 4410 (3.2) $\dfrac{6!}{8} \times 49$ Tina Redlinger, 12/07 Olathe, KS |
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| 4508 (2.0) $98 \times 46$ Brooke Atkinson, 4/09 Olathe, KS |
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| 4608 (2.0) $48 \times 96$ Katie Ware, 1/07 Overland Park, KS |
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| 4633 (3.2) $\sqrt{68^4} + 9$ Andisheh Ataollahi, 10/06 Overland Park, KS |
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| 4689 (2.0) $4689$ Allison Layne-Mulhern, 11/13 Overland Park, KS |
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| 4698 (2.0) $4698$ Bruno Biazetto, 4/17 Overland Park, KS |
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| 4761 (3.0) $69^{8/4}$ Yunxia Qi, 7/12 Lawrence, KS |
4769 (3.2) $\sqrt{69^4} + 8$ Zach Alholm, 11/06 Overland Park, KS |
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| 5364 (2.0) $894 \times 6$ Bryce Torres, 9/06 Perryton, TX |
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| 5552 (2.0) $694 \times 8$ Katie Ware, 1/07 Overland Park, KS |
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| 5688 (2.0) $948 \times 6$ Katie Ware, 2/07 Overland Park, KS |
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| 5696 (2.0) $64 \times 89$ Brooke Atkinson, 4/09 Olathe, KS |
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| 5796 (2.0) $69 \times 84$ Ashlin Hadenfeld, 9/06 Overland Park, KS |
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| 5832 (2.0) $648 \times 9$ Zach Alholm, 11/06 Overland Park, KS |
5836 (3.2) $8 \times \sqrt{9^6} + 4$ Rebecca Stewart, 11/07 Lenexa, Kansas |
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| 5904 (2.0) $984 \times 6$ Shawn Graf, 11/06 Overland Park, KS |
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| 6272 (2.0) $64 \times 98$ Cara Seats, 10/07 Lawrence, KS |
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| 6392 (2.0) $94 \times 68$ Katie Cooper, 9/04 Stilwell, KS |
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| 6489 (2.0) $6489$ Bruno Biazetto, 4/17 Overland Park, KS |
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| 6493 (3.0) $9^4 - 68$ Andisheh Ataollahi, 11/06 Overland Park, KS |
6498 (2.0) $6498$ Bruno Biazetto, 4/17 Overland Park, KS |
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| 6547 (3.0) $9^4 - 8 - 6$ Kimberly Grosdidier, 10/05 Eudora, KS |
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| 6563 (3.0) $9^4 + 8 - 6$ Katie Ware, 2/07 Overland Park, KS |
6567 (3.0) $9^{8-4} + 6$ Apollo Okwuone, 12/04 Olathe, KS |
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| 6629 (3.0) $9^4 + 68$ Andisheh Ataollahi, 11/06 Overland Park, KS |
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| 6849 (2.0) $6849$ Bruno Biazetto, 4/17 Overland Park, KS |
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| 6894 (2.0) $6894$ Bruno Biazetto, 4/17 Overland Park, KS |
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| 7405 (3.2) $\sqrt{86^4} + 9$ Andisheh Ataollahi, 10/06 Overland Park, KS |
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| 7568 (2.0) $946 \times 8$ Bryce Torres, 9/06 Perryton, TX |
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| 7614 (2.0) $846 \times 9$ Zach Alholm, 11/06 Overland Park, KS |
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| 7712 (2.0) $964 \times 8$ Bryce Torres, 12/06 Perryton, TX |
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| 7776 (2.0) $864 \times 9$ Ashlin Hadenfeld, 9/06 Overland Park, KS |
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| 8064 (2.0) $84 \times 96$ Emily Winchester, 1/05 Olathe, KS |
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| 8084 (2.0) $94 \times 86$ Ashlin Hadenfeld, 9/06 Overland Park, KS |
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| 8748 (3.0) $9^4 \times \dfrac86$ Ashlin Hadenfeld, 9/06 Overland Park, KS |
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| 9224 (3.2) $\sqrt{96^4} + 8$ Andisheh Ataollahi, 10/06 Overland Park, KS |
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| 9610 (3.2) $\sqrt{98^4} + 6$ Andisheh Ataollahi, 10/06 Overland Park, KS |
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| 10368 (3.2) $4! \times 6 \times 8 \times 9$ Anthony Sands, 3/06 Raytown, MO |
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| 10680 (5.4) $\dfrac{-89 \times 4!}{\tanh\ln\sqrt{.\overline{6}}}$ Steve Wilson, 6/22 Lawrence, KS |
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| 13122 (3.0) $9^4 \times (8 - 6)$ Kacie Malin, 9/07 Shawnee, KS |
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| 14641 (3.0) $(9 + 8 - 6)^4$ Kimberly Grosdidier, 10/05 Eudora, KS |
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| 15120 (3.2) $6! \times (4 + 8 + 9)$ Zach Alholm, 10/06 Leawood, KS |
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| 20160 (3.2) $\dfrac{9!}{8+6+4}$ Rabeh Ghadiri, 11/08 Overland Park, KS |
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| 22032 (3.0) $6^4 \times (8 + 9)$ Zach Burger, 5/05 Overland Park, KS |
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| 31104 (3.2) $8 \times 6^4 \times \sqrt{9}$ Tiffany Copple, 1/07 Overland Park, KS |
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| 32759 (3.0) $4^6 \times 8 - 9$ Christie Birzer, 2/06 Shawnee, KS |
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| 32767 (3.4) $4^6 \times 8 - .\overline{9}$ Rabeh Ghadiri, 9/08 Overland Park, KS |
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| 39370 (3.2) $6 \times \sqrt{9^8} + 4$ Rebecca Stewart, 11/07 Lenexa, Kansas |
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| 40277 (3.4) $8! + \sqrt{9} - 46$ Ross Andring, 10/06 Osawatomie, KS |
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| 40321 (3.2) $8! - 9 + 6 + 4$ Andisheh Ataollahi, 12/06 Overland Park, KS |
40326 (3.2) $8! + 4 \times \dfrac96$ Andisheh Ataollahi, 12/06 Overland Park, KS |
40327 (3.2) $8! + 9 - 6 + 4$ Andisheh Ataollahi, 12/06 Overland Park, KS |
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| 40339 (3.2) $8! + 9 + 6 + 4$ Andisheh Ataollahi, 12/06 Overland Park, KS |
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| 41073 (3.6) $8! + 6! + 4! + 9$ Wei Zhang, 7/12 Lawrence, KS |
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| 41134 (3.4) $8! + 6! + 94$ Katie Cooper, 12/04 Stilwell, KS |
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| 45370 (3.2) $\dfrac{9!}{8} + 6 + 4$ Rabeh Ghadiri, 11/08 Overland Park, KS |
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| 50617 (3.0) $(6 + 9)^4 - 8$ Kimberly Grosdidier, 10/05 Eudora, KS |
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| 52488 (3.2) $(6 + \sqrt{9})^4 \times 8$ Jonathan Finlay, 5/05 Shawnee, KS |
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| 65551 (3.0) $4^8 + 6 + 9$ Cameron Haines, 5/06 Olathe, KS |
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| 83527 (3.0) $(9 + 8)^4 + 6$ Cameron Haines, 4/06 Olathe, KS |
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| 93312 (3.0) $6^4 \times 8 \times 9$ Tiffany Copple, 3/07 Overland Park, KS |
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| 97344 (3.2) $46^{\sqrt{9}} + 8$ Zach Alholm, 11/06 Overland Park, KS |
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| 98304 (3.0) $4^8 \times \dfrac96$ Yunxia Qi, 7/12 Lawrence, KS |
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| 103680 (3.2) $6! \times 8 \times 9 \times \sqrt{4}$ Tim Sackett, 4/05 Belton, MO |
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| 131072 (3.0) $\dfrac{4^9}{8-6}$ Shawn Graf, 11/06 Overland Park, KS |
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| 155520 (3.8) $\dfrac{9!}{8!} \times 6! \times 4!$ Darren Boss, 4/03 Shawnee, KS |
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| 185761 (3.0) $431^2$ Scott Dixon, 9/07 Lenexa, KS |
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| 221184 (3.0) $8^4 \times 6 \times 9$ Tiffany Copple, 3/07 Overland Park, KS |
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| 234256 (3.0) $(23 - 1)^4$ Scott Dixon, 9/07 Lenexa, KS |
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| 262151 (3.2) $8^6 + \sqrt{49}$ Sydney Barker, 5/03 Stilwell, KS |
262152 (3.2) $\sqrt{64^9} + 8$ Andisheh Ataollahi, 10/06 Overland Park, KS |
262158 (3.0) $4^9 + 6 + 8$ Shawn Graf, 11/06 Overland Park, KS |
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| 262192 (3.0) $4^9 + 6 \times 8$ Adam McAdoo, 5/05 Lenexa, KS |
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| 262230 (3.0) $4^9 + 86$ Tiffany Copple, 1/07 Overland Park, KS |
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| 268705 (3.0) $9^4 + 8^6$ Jonathan Finlay, 5/05 Shawnee, KS |
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| 279841 (3.0) $(6 + 8 + 9)^4$ Frederick Agbomanyi, 11/04 Shawnee, KS |
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| 294912 (3.0) $4^6 \times 8 \times 9$ Tiffany Copple, 3/07 Overland Park, KS |
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| 314928 (3.0) $9^4 \times 6 \times 8$ Tiffany Copple, 3/07 Overland Park, KS |
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| 331776 (3.0) $(23 + 1)^4$ Scott Dixon, 9/07 Lenexa, KS |
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| 366984 (3.2) $9! + 4^6 + 8$ Ross Andring, 10/06 Osawatomie, KS |
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| 373248 (3.4) $(\sqrt{4} \times \sqrt{9})^6 \times 8$ Renato Bacco, 10/07 Overland Park, KS |
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| 401408 (3.0) $4^6 \times 98$ Katie Ware, 2/07 Overland Park, KS |
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| 403944 (3.8) $9! + 8! + 6! + 4!$ Tiffany Copple, 4/07 Overland Park, KS |
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| 531357 (3.0) $9^6 - 84$ Andisheh Ataollahi, 11/06 Overland Park, KS |
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| 531393 (3.0) $9^6 - 48$ Ross Andring, 10/06 Osawatomie, KS |
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| 531437 (3.0) $9^6 + 4 - 8$ Kimberly Grosdidier, 10/05 Eudora, KS |
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| 531445 (3.0) $9^6 + 8 - 4$ Katie Cooper, 8/04 Stilwell, KS |
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| 531489 (3.0) $9^6 + 48$ Cameron Haines, 5/06 Olathe, KS |
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| 531525 (3.0) $9^6 + 84$ Cameron Haines, 5/06 Olathe, KS |
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| 535537 (3.0) $8^4 + 9^6$ Marcela Perez, 11/08 Spring Hill, KS |
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| 983040 (3.0) $4^8 \times (6 + 9)$ Rahel Frew, 2/07 Olathe, KS |
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| 1062882 (3.0) $9^6 \times \dfrac84$ Zach Alholm, 10/06 Leawood, KS |
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| 1179648 (3.2) $4^8 \times \sqrt{9} \times 6$ Ross Andring, 10/06 Osawatomie, KS |
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| 1244160 (3.4) $9 \times 8 \times 6! \times 4!$ Yunxia Qi, 7/12 Lawrence, KS |
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| 1679616 (3.0) $\left( \dfrac{4 \times 9}{6} \right)^8$ Andisheh Ataollahi, 12/06 Overland Park, KS |
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| 1679622 (3.2) $\sqrt{ (4 \times 9)^8} + 6$ Renato Bacco, 10/07 Overland Park, KS |
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| 2313441 (3.0) $(6 \times 8 - 9)^4$ Cameron Haines, 5/06 Olathe, KS |
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| 2903040 (4.2) $9! \times 8 \times \log(6 + 4)$ Tiffany Copple, 4/07 Overland Park, KS |
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| 3538944 (3.0) $4^8 \times 6 \times 9$ Tiffany Copple, 3/07 Overland Park, KS |
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| 4251528 (3.2) $\dfrac{(9 \times \sqrt{4})^6}{8}$ Jonathan Finlay, 5/05 Shawnee, KS |
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| 4478976 (3.0) $\dfrac{(9 \times 8)^4}{6}$ Jonathan Finlay, 5/05 Shawnee, KS |
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| 10616832 (3.0) $\dfrac{96^4}{8}$ Katie Ware, 2/07 Overland Park, KS |
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| 12117361 (3.0) $(68 - 9)^4$ Kashmira Sayani, 1/17 Overland Park, KS |
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| 20155392 (3.0) $\dfrac84 \times 6^9$ Tiffany Copple, 4/07 Overland Park, KS |
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| 22544384 (3.0) $4^9 \times 86$ Jonathan Finlay, 5/05 Shawnee, KS |
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| 26873862 (3.0) $(9 \times 8)^4 + 6$ Cameron Haines, 4/06 Olathe, KS |
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| 34012224 (3.0) $\left( \dfrac{8 \times 9}{4} \right)^6$ Frederick Agbomanyi, 10/04 Shawnee, KS |
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| 43045425 (3.0) $9^8 - 6^4$ Renato Bacco, 10/07 Overland Park, KS |
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43046675 (3.0) $9^8 - 46$ Andisheh Ataollahi, 11/06 Overland Park, KS |
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| 43046719 (3.0) $9^8 + 4 - 6$ Cameron Haines, 3/06 Olathe, KS |
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| 43046721 (4.0) $9^8 \times \log(6 + 4)$ Tiffany Copple, 4/07 Overland Park, KS |
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| 43048017 (3.0) $9^8 + 6^4$ Yunxia Qi, 7/12 Lawrence, KS |
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| 92897280 (3.4) $96 \times 4! \times 8!$ Ross Andring, 10/06 Osawatomie, KS |
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| 376453446 (3.0) $89^4 \times 6$ Marcela Perez, 11/08 Spring Hill, KS |
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| 900000000 (3.0) $9 \times (4 + 6)^8$ Renato Bacco, 10/07 Overland Park, KS |
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| 1000000000 (3.0) $(8 - 4 + 6)^9$ Kimberly Grosdidier, 11/05 Eudora, KS |
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| 1073741824 (3.2) $8 \times \sqrt{64^9}$ Rebecca Stewart, 11/07 Lenexa, Kansas |
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1073741833 (3.0) $8^{4+6} + 9$ Tiffany Copple, 4/07 Overland Park, KS |
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| 1342177280 (3.0) $(6 + 4) \times 8^9$ Yunxia Qi, 7/12 Lawrence, KS |
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| 1980149166 (3.0) $9^8 \times 46$ Katie Cooper, 10/04 Stilwell, KS |
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| 2176782336 (3.0) $9^6 \times 8^4$ Marcela Perez, 11/08 Spring Hill, KS |
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| little googol (3.6) $\left( \dfrac84 \right)^{6/((\sqrt{9})!\%)}$ Ralph Jeffords, 5/08 Centreville, VA |
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| googol (3.2) $\sqrt[(9-8)\%]{4+6}$ Paolo Pellegrini, 7/08 Martina Franca, Italy |
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| googolplex (4.4) $(4+6)^{ \sqrt[-8\%]{.\overline{9}\% \pm\pmf\phantom8}}$ Paolo Pellegrini, 1/09 Martina Franca, Italy |
Page 1 (1-400), Page 2 (401-800), Page 3 (801-1200), Page 4 (1201+).