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Four fours is a classic problem, dating back at least 90 years. Create each of the positive integers using four copies of 4, 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 (1601-2000), Page 6 (2001+).
| 2001 (2.8) $\dfrac{4 + 4 + .4\%}{.4\%}$ Steve Wilson, 9/23 Lawrence, KS |
2002 (3.4) $\dfrac{4 + 4}{4\pmf} + \sqrt{4}$ Steve Wilson, 9/23 Lawrence, KS |
2003 (4.0) $\dfrac{4}{(\sqrt{4})\pmf} + \sqrt{\dfrac{4}{.\overline{4}}}$ Steve Wilson, 9/23 Lawrence, KS |
2004 (2.4) $\dfrac{4 + 4}{.4\%} + 4$ Steve Wilson, 9/23 Lawrence, KS |
2005 (3.8) $\dfrac{4}{(\sqrt{4})\pmf} + \dfrac{\sqrt{4}}{.4}$ Steve Wilson, 9/23 Lawrence, KS |
2006 (3.6) $\dfrac{4}{(\sqrt{4})\pmf} + \dfrac{4!}{4}$ Steve Wilson, 9/23 Lawrence, KS |
2008 (3.4) $\dfrac{4}{(\sqrt{4})\pmf} + 4 + 4$ Steve Wilson, 9/23 Lawrence, KS |
2009 (3.8) $\dfrac{4}{(\sqrt{4})\pmf} + \dfrac{4}{.\overline{4}}$ Steve Wilson, 9/23 Lawrence, KS |
2010 (2.6) $\dfrac{4 + 4 + 4\%}{.4\%}$ Steve Wilson, 9/23 Lawrence, KS |
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| 2048 (3.0) $(4 + 4) \times 4^4$ Isaac Grosof, 2/09 Mercer Island, WA |
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| 2177 (4.4) $\cosh(4 \times \arcosh 4) + 4^4$ Steve Wilson, 9/23 Lawrence, KS |
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| 2220 (3.4) $\dfrac{4.44}{(\sqrt{4}) ‰}$ Steve Wilson, 11/09 Raytown, MO |
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| 2222 (4.2) $\dfrac{4.\overline{4} - .\overline{4} ‰}{(\sqrt{4}) ‰}$ Steve Wilson, 11/09 Raytown, MO |
2225 (4.2) $\dfrac{4 + \dfrac{\sqrt{4\%}}{.\overline{4}}}{(\sqrt{4}) ‰}$ Steve Wilson, 11/09 Raytown, MO |
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| 2270 (4.2) $\dfrac{4 + \dfrac{4!\%}{.\overline{4}}}{(\sqrt{4}) ‰}$ Steve Wilson, 11/09 Raytown, MO |
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| 2288 (4.0) $\dfrac{4 + 4! \times 4! ‰}{(\sqrt{4}) ‰}$ Steve Wilson, 11/09 Raytown, MO |
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| 2304 (3.8) $(4! + 4!) \times (4! + 4!)$ Tim Murphy, 4/03 Olathe, KS |
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| 2400 (3.6) $(4! \times 4! + 4!) \times 4$ Zach Warring, 10/09 Olathe, KS |
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| 2475 (2.6) $\dfrac{44}{4 \times .\overline{4}\%}$ David Barksdale, 3/09 Kirkland, WA |
2480 (3.8) $\dfrac{4 + 4! \times 4\%}{(\sqrt{4}) ‰}$ Steve Wilson, 10/09 Raytown, MO |
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| 2640 (3.8) $4 \times \dfrac{44}{\sqrt{.\overline{4}\%}}$ David Barksdale, 3/09 Kirkland, WA |
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| 2700 (2.6) $\dfrac{4 \times 4 - 4}{.\overline{4}\%}$ David Barksdale, 3/09 Kirkland, WA |
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| 2880 (3.6) $(4 \times 4! + 4!) \times 4!$ Steve Wilson, 11/09 Raytown, MO |
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| 3456 (3.4) $\dfrac{4!^4}{4! \times 4}$ Ron Palcic, 8/03 Olathe, KS |
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| 4092 (3.0) $(4 + 4)^4 - 4$ Apollo Okwuone, 2/03 Olathe, KS |
4096 (3.0) $4^4 \times 4 \times 4$ Cassie Weatherwax, 2/03 Lawrence, KS |
4100 (3.0) $(4 + 4)^4 + 4$ Eric Millard, 5/07 Olathe, KS |
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| 4224 (3.2) $4! \times 44 \times 4$ Nora Osley, 10/08 New York, NY |
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| 4400 (2.2) $44 \times \dfrac{4}{4\%}$ Dave Jones, 7/07 Coventry, England |
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| 4444 (2.0) $4444$ Anders Skjäl, 4/04 Turku, Finland |
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| 4500 (2.6) $\dfrac{4 \times 4 + 4}{.\overline{4}\%}$ David Barksdale, 3/09 Kirkland, WA |
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| 4608 (3.6) $(4! + 4!) \times 4! \times 4$ Jackie Shirley, 10/09 Olathe, KS |
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| 5184 (3.2) $4 \times \left( \dfrac{4!}{4} \right)^4$ Marc Carreras-Vidal, 8/15 Maó, Spain |
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| 6120 (3.4) $4^4 \times 4! - 4!$ Josh Crow, 1/09 Lenexa, KS |
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6140 (3.2) $4^4 \times 4! - 4$ Jeremy Miller, 8/07 Olathe, KS |
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| 6148 (3.2) $4^4 \times 4! + 4$ Jeremy Miller, 8/07 Olathe, KS |
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| 6168 (3.4) $4^4 \times 4! + 4!$ Josh Crow, 1/09 Lenexa, KS |
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| 6660 (3.8) $\dfrac{444}{\sqrt{.\overline{4}\%}}$ David Barksdale, 3/09 Kirkland, WA |
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| 7744 (3.2) $4 \times \sqrt{44^4}$ Regina Hillman, 10/07 Bucyrus, KS |
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| 9000 (2.6) $\dfrac{44 - 4}{.\overline{4}\%}$ David Barksdale, 3/09 Kirkland, WA |
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| 10000 (7.6) $\dfrac{\sqrt{4^{4!!}}}{.4^4}$ Bruce Manoly, 4/24 Crescent City, CA |
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| 11100 (2.2) $\dfrac{444}{4\%}$ Dave Jones, 9/06 Coventry, England |
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| 11264 (3.0) $44 \times 4^4$ Joseph Mavungu, 5/03 Olathe, KS |
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| 12288 (3.4) $4^4 \times 4! \times \sqrt{4}$ Jeremy Miller, 8/07 Olathe, KS |
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| 13800 (3.8) $4! \times 4! \times 4! - 4!$ Zach Warring, 9/09 Olathe, KS |
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| 13820 (3.6) $4! \times 4! \times 4! - 4$ Jeremy Miller, 9/07 Olathe, KS |
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| 13828 (3.6) $4! \times 4! \times 4! + 4$ Jeremy Miller, 9/07 Olathe, KS |
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| 13848 (3.8) $4! \times 4! \times 4! + 4!$ Zach Warring, 9/09 Olathe, KS |
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| 14641 (3.0) $\left( \dfrac{44}{4} \right)^4$ Brian Nixt, 3/06 Lenexa, KS |
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| 16384 (3.0) $\dfrac{4^{4+4}}{4}$ Joseph Mavungu, 3/03 Olathe, KS |
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| 20625 (9.2) $\dfrac{\left(\arcsec\sqrt{4}\right)!!!!! \times (4!!)!!!!}{((4!!)!!!)!!!!!!!!!! \times \arccsc\sqrt{\sqrt{4}}}$ Bruce Manoly, 4/24 Crescent City, CA |
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| 20736 (3.0) $(4 + 4 + 4)^4$ Jeremy Miller, 9/07 Olathe, KS |
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| 24576 (3.2) $4^4 \times 4! \times 4$ Jeremy Miller, 8/07 Olathe, KS |
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| 25344 (3.4) $4! \times 4! \times 44$ Zach Warring, 9/09 Olathe, KS |
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| 25600 (3.2) $\dfrac{4}{4\%} \times 4^4$ Nathaniel Uhl, 9/07 Olathe, KS |
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| 27648 (3.8) $4! \times 4! \times 4! \times \sqrt{4}$ Zach Warring, 10/09 Olathe, KS |
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| 40000 (3.2) $\dfrac{(4! - 4)^4}{4}$ Zach Warring, 10/09 Olathe, KS |
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| 55296 (3.6) $4! \times 4! \times 4! \times 4$ Zach Warring, 10/09 Olathe, KS |
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| 65532 (3.0) $4^{4+4} - 4$ Adam Petrowsky, 4/03 Lenexa, KS |
65536 (3.0) $4^4 \times 4^4$ Sydney Barker, 1/03 Stilwell, KS |
65540 (3.2) $\sqrt{4^{4 \times 4}} + 4$ Sydney Barker, 4/03 Stilwell, KS |
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| 82940 (3.2) $\dfrac{4!^4}{4} - 4$ Jackie Shirley, 10/09 Olathe, KS |
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| 82948 (3.2) $\dfrac{4!^4}{4} + 4$ Zach Warring, 9/09 Olathe, KS |
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| 85184 (3.4) $\sqrt{44^{4 + \sqrt{4}}}$ Brian Nixt, 3/06 Lenexa, KS |
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| 147456 (3.4) $4^4 \times 4! \times 4!$ Josh Crow, 1/09 Lenexa, KS |
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| 153664 (3.2) $\dfrac{(4! + 4)^4}{4}$ Zach Warring, 10/09 Olathe, KS |
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| 197136 (3.2) $\sqrt{444^4}$ Brian Nixt, 3/06 Lenexa, KS |
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| 262144 (3.0) $4 \times 4^{4+4}$ Nathaniel Uhl, 9/07 Olathe, KS |
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| 331776 (3.8) $4! \times 4! \times 4! \times 4!$ Darren Boss, 4/03 Shawnee, KS |
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| 331784 (3.2) $4!^4 + 4 + 4$ Jackie Shirley, 10/09 Olathe, KS |
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| 663552 (3.4) $4!^4 + 4!^4$ Rabeh Ghadiri, 9/08 Overland Park, KS |
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| 937024 (3.0) $\dfrac{44^4}{4}$ Katie Cooper, 10/04 Stilwell, KS |
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| 1327104 (3.4) $\dfrac{(4! + 4!)^4}{4}$ Jackie Shirley, 10/09 Olathe, KS |
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| 1874048 (3.2) $\dfrac{44^4}{\sqrt{4}}$ Jackie Shirley, 10/09 Olathe, KS |
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| 3748072 (3.2) $44^4 - 4!$ Josh Crow, 1/09 Lenexa, KS |
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| 3748092 (3.0) $44^4 - 4$ Ian Bowdler, 10/07 Solihull, England |
3748096 (3.2) $\sqrt{44^{4+4}}$ Brian Nixt, 3/06 Lenexa, KS |
3748100 (3.0) $44^4 + 4$ Kimberly Grosdidier, 12/05 Overland Park, KS |
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| 3748120 (3.2) $44^4 + 4!$ Adam McAdoo, 5/05 Lenexa, KS |
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| 5308416 (3.0) $(44 + 4)^4$ Zach Warring, 9/09 Olathe, KS |
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| 9370240 (3.2) $\dfrac{44^4}{.4}$ Ian Bowdler, 10/07 Solihull, England |
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| 14992384 (3.0) $44^4 \times 4$ Shelbi Russell, 5/05 Merriam, KS |
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| 16777216 (3.0) $(4 \times 4 \times 4)^4$ Sydney Barker, 2/03 Stilwell, KS |
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| 429981696 (3.4) $\left( \dfrac{4! \times 4!}{4} \right)^4$ Rabeh Ghadiri, 12/08 Overland Park, KS |
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| 959512576 (3.0) $(4 \times 44)^4$ Kashmira Sayani, 3/17 Overland Park, KS |
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| 1073741824 (3.0) $\dfrac{4^{4 \times 4}}{4}$ Evan Meyers, 10/10 Eudora, KS |
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| 4294967272 (3.2) $4^{4 \times 4} - 4!$ Josh Crow, 2/09 Lenexa, KS |
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| 4294967292 (3.0) $4^{4 \times 4} - 4$ Josh Crow, 2/09 Lenexa, KS |
4294967300 (3.0) $4^{4 \times 4} + 4$ Josh Crow, 2/09 Lenexa, KS |
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| 4294967320 (3.2) $4^{4 \times 4} + 4!$ Josh Crow, 2/09 Lenexa, KS |
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| 38862602496 (3.0) $444^4$ Ian Bowdler, 10/07 Solihull, England |
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| 103079215104 (3.2) $4^{4 \times 4} \times 4!$ Josh Crow, 2/09 Lenexa, KS |
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| googol (3.4) $\left( \dfrac{4}{.4} \right)^{4/(4\%)}$ Brian Hollenbeck, 5/03 Emporia, KS |
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| googolplex (5.8) $\left( \dfrac{4}{.4} \right)^{\sqrt[-4\%]{\left( \tan \operatorname{arcsec} \sqrt{\sqrt{4}} \right) \%\%}}$ Ralph Jeffords, 2/09 Centreville, VA |
Page 1 (1-400), Page 2 (401-800), Page 3 (801-1200), Page 4 (1201-1600), Page 5 (1601-2000), Page 6 (2001+).