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This problem was proposed by Integermaniac master Paolo Pellegrini. Create each of the positive integers using four copies of 1, 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.
PREVIOUS Page, Page 26 (10001+), ... Index to All Pages.
| 10001 (2.4) $\dfrac{1}{1\%\%} + 1 \times 1$ Jonathan Frank, 3/21 Rye, NY |
10002 (2.4) $\dfrac{1}{1\%\%} + 1 + 1$ Jonathan Frank, 3/21 Rye, NY |
10010 (2.6) $\dfrac{1}{1\%\%} + \dfrac{1}{.1}$ Jonathan Frank, 3/21 Rye, NY |
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| 10011 (2.4) $\dfrac{1}{1\%\%} + 11$ Jonathan Frank, 3/21 Rye, NY |
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| 10100 (2.6) $\dfrac{1}{1\%\%} + \dfrac{1}{1\%}$ Jonathan Frank, 3/21 Rye, NY |
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| 10295 (5.4) $11!! - \dfrac{1}{1\%}$ Jonathan Frank, 3/21 Rye, NY |
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| 10384 (5.2) $11!! - 11$ Jonathan Frank, 3/21 Rye, NY |
10385 (5.4) $11!! - \dfrac{1}{.1}$ Jonathan Frank, 3/21 Rye, NY |
10386 (5.6) $11!! - \dfrac{1}{.\overline{1}}$ Jonathan Frank, 3/21 Rye, NY |
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| 10392 (5.6) $11!! - \log \left( \dfrac{1}{1 \pmf} \right)$ Jonathan Frank, 3/21 Rye, NY |
10393 (5.2) $11!! - 1 - 1$ Jonathan Frank, 3/21 Rye, NY |
10394 (5.2) $11!! - 1 \times 1$ Jonathan Frank, 3/21 Rye, NY |
10395 (5.2) $11!! \times 1 \times 1$ Jonathan Frank, 3/21 Rye, NY |
10396 (5.2) $11!! + 1 \times 1$ Jonathan Frank, 3/21 Rye, NY |
10397 (5.2) $11!! + 1 + 1$ Jonathan Frank, 3/21 Rye, NY |
10398 (5.6) $11!! + \log \left( \dfrac{1}{1 \pmf} \right)$ Jonathan Frank, 3/21 Rye, NY |
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| 10404 (5.6) $11!! + \dfrac{1}{.\overline{1}}$ Jonathan Frank, 3/21 Rye, NY |
10405 (5.4) $11!! + \dfrac{1}{.1}$ Jonathan Frank, 3/21 Rye, NY |
10406 (5.6) $11!! + 11$ Jonathan Frank, 3/21 Rye, NY |
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| 10495 (5.4) $11!! + \dfrac{1}{1\%}$ Jonathan Frank, 3/21 Rye, NY |
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| 11000 (2.4) $\dfrac{11}{.1 \times 1\%}$ Luke Sauvadon, 6/12 Lawrence, KS |
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| 11100 (2.2) $\dfrac{111}{1\%}$ Lisa Fisher, 7/09 Lawrence, KS |
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| 11395 (5.4) $11!! + \dfrac{1}{1 \pmf}$ Jonathan Frank, 3/21 Rye, NY |
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| 11520 (6.0) $\left( \dfrac{1}{.1} \right)!! \times \sqrt{\dfrac{1}{.\overline{1}}}$ Jonathan Frank, 3/21 Rye, NY |
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| 11550 (5.8) $11!! \times \dfrac{.\overline{1}}{.1}$ Jonathan Frank, 3/21 Rye, NY |
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| 12000 (3.2) $\dfrac{11 + 1}{1 \pmf}$ Jonathan Frank, 3/21 Rye, NY |
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| 16384 (5.0) $(-\log{(1\%)})^{11-\log{(1\pm)}}$ Jonathan Frank, 3/21 Rye, NY |
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| 19683 (5.0) $(-\log{(1 \pm)})^{11 + \log{(1 \%)}}$ Jonathan Frank, 3/21 Rye, NY |
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| 20790 (5.2) $11!! \times (1 + 1)$ Jonathan Frank, 3/21 Rye, NY |
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| 31185 (5.6) $11!! \times \log \left( \dfrac{1}{1 \pmf} \right)$ Jonathan Frank, 3/21 Rye, NY |
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| 34560 (5.8) $\left( \dfrac{1}{.1} \right)!! \times \dfrac{1}{.\overline{1}}$ Jonathan Frank, 3/21 Rye, NY |
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| 34650 (6.0) $\dfrac{11!!}{.1} \times \sqrt{.\overline{1}}$ Jonathan Frank, 3/21 Rye, NY |
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| 36287 (3.4) $(11 - 1)! \% - 1$ Jonathan Frank, 3/21 Rye, NY |
36288 (3.4) $(11 - 1)! \% \times 1$ Jonathan Frank, 3/21 Rye, NY |
36289 (3.4) $(11 - 1)! \% + 1$ Jonathan Frank, 3/21 Rye, NY |
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| 38400 (5.6) $\left( \dfrac{1}{.1} \right)!! \times \dfrac{1}{.1}$ Jonathan Frank, 3/21 Rye, NY |
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| 42240 (5.4) $\left( \dfrac{1}{.1} \right)!! \times 11$ Jonathan Frank, 3/21 Rye, NY |
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| 44351 (3.8) $11!\% \times .\overline{1} - 1$ Jonathan Frank, 3/21 Rye, NY |
44352 (3.8) $11! \times .\overline{1} \times 1\%$ Jonathan Frank, 3/21 Rye, NY |
44353 (3.8) $11!\% \times .\overline{1} + 1$ Jonathan Frank, 3/21 Rye, NY |
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| 44800 (4.2) $\left( \dfrac{1}{.1} \right)! \times .\overline{1} \times .\overline{1}$ Jonathan Frank, 3/21 Rye, NY |
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| 46079 (5.2) $(11 + 1)!! - 1$ Jonathan Frank, 3/21 Rye, NY |
46080 (5.2) $(11 + 1)!! \times 1$ Jonathan Frank, 3/21 Rye, NY |
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| 46081 (5.2) $(11 + 1)!! + 1$ Jonathan Frank, 3/21 Rye, NY |
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| 51975 (5.6) $\dfrac{11!!}{.1 + .1}$ Jonathan Frank, 3/21 Rye, NY |
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| 54000 (3.8) $\dfrac{(1 + 1 + 1)!}{.\overline{1}\pmf}$ Jonathan Frank, 3/21 Rye, NY |
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| 59049 (4.6) $(-\log{(1 \pm)})^{11-1}$ Jonathan Frank, 3/21 Rye, NY |
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| 64800 (4.2) $\dfrac{((1 + 1 + 1)!)!\%}{.\overline{1}\pmf}$ Jonathan Frank, 3/21 Rye, NY |
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| 93552 (6.0) $\dfrac{11!!}{.\overline{1}} + \log{(1 \pm)}$ Jonathan Frank, 3/21 Rye, NY |
93553 (6.0) $\dfrac{11!!}{.\overline{1}} + \log{(1 \%)}$ Jonathan Frank, 3/21 Rye, NY |
93554 (5.6) $\dfrac{11!!}{.\overline{1}} - 1$ Jonathan Frank, 3/21 Rye, NY |
93555 (5.6) $11!! \times \dfrac{1}{.\overline{1}}$ Jonathan Frank, 3/21 Rye, NY |
93556 (5.6) $\dfrac{11!!}{.\overline{1}} + 1$ Jonathan Frank, 3/21 Rye, NY |
93557 (6.0) $\dfrac{11!!}{.\overline{1}} - \log{(1 \%)}$ Jonathan Frank, 3/21 Rye, NY |
93558 (6.0) $\dfrac{11!!}{.\overline{1}} - \log{(1 \pm)}$ Jonathan Frank, 3/21 Rye, NY |
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| 94500 (5.8) $\left( \dfrac{1}{.\overline{1}} \right)!! \times \dfrac{1}{1\%}$ Jonathan Frank, 3/21 Rye, NY |
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| 100000 (3.4) $\dfrac{1}{1\%} \times \dfrac{1}{1 \pmf}$ Jonathan Frank, 3/21 Rye, NY |
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| 103947 (5.8) $\dfrac{11!!}{.1} + \log(1 \pm)$ Jonathan Frank, 3/21 Rye, NY |
103948 (5.8) $\dfrac{11!!}{.1} + \log(1 \%)$ Jonathan Frank, 3/21 Rye, NY |
103949 (5.4) $\dfrac{11!!}{.1} - 1$ Jonathan Frank, 3/21 Rye, NY |
103950 (5.4) $11!! \times \dfrac{1}{.1}$ Jonathan Frank, 3/21 Rye, NY |
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| 103951 (5.4) $\dfrac{11!!}{.1} + 1$ Jonathan Frank, 3/21 Rye, NY |
103952 (5.8) $\dfrac{11!!}{.1} - \log(1 \%)$ Jonathan Frank, 3/21 Rye, NY |
103953 (5.8) $\dfrac{11!!}{.1} - \log(1 \pm)$ Jonathan Frank, 3/21 Rye, NY |
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| 111000 (2.4) $\dfrac{111}{.1\%}$ Lisa Fisher, 7/09 Lawrence, KS |
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| 114345 (5.2) $11!! \times 11$ Jonathan Frank, 3/21 Rye, NY |
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| 133055 (4.0) $11!\% \times \sqrt{.\overline{1}} - 1$ Jonathan Frank, 3/21 Rye, NY |
133056 (4.0) $11!\% \times \sqrt{.\overline{1}} \times 1$ Jonathan Frank, 3/21 Rye, NY |
133057 (4.0) $11!\% \times \sqrt{.\overline{1}} + 1$ Jonathan Frank, 3/21 Rye, NY |
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| 135135 (5.2) $(11 + 1 + 1)!!$ Jonathan Frank, 3/21 Rye, NY |
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| 161050 (3.4) $\sqrt[.1]{\sqrt{11}} - 1$ Jonathan Frank, 3/21 Rye, NY |
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| 161051 (3.4) $\sqrt[.1]{\sqrt{11}} \times 1$ Jonathan Frank, 3/21 Rye, NY |
161052 (3.4) $\sqrt[.1]{\sqrt{11}} + 1$ Jonathan Frank, 3/21 Rye, NY |
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| 177144 (5.0) $(-\log{(1 \pm)})^{11} + \log{(1 \pm)}$ Jonathan Frank, 3/21 Rye, NY |
177145 (5.0) $(-\log{(1 \pm)})^{11} + \log{(1 \%)}$ Jonathan Frank, 3/21 Rye, NY |
177146 (4.6) $(-\log{(1 \pm)})^{11} - 1$ Jonathan Frank, 3/21 Rye, NY |
177147 (4.4) $\left( \log \left( \dfrac{1}{1 \pmf} \right)\right)^{11}$ Jonathan Frank, 3/21 Rye, NY |
177148 (4.6) $(-\log{(1 \pm)})^{11} + 1$ Jonathan Frank, 3/21 Rye, NY |
177149 (5.0) $(-\log{(1 \pm)})^{11} - \log{(1 \%)}$ Jonathan Frank, 3/21 Rye, NY |
177150 (5.0) $(-\log{(1 \pm)})^{11} - \log{(1 \pm)}$ Jonathan Frank, 3/21 Rye, NY |
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| 181440 (3.6) $\dfrac{ \left( \dfrac{1}{.\overline{1}} \right)!}{1 + 1}$ Jonathan Frank, 3/21 Rye, NY |
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| 199584 (3.4) $\dfrac{11!\%}{1 + 1}$ Jonathan Frank, 3/21 Rye, NY |
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| 384000 (5.6) $\left( \dfrac{1}{.1} \right)!! \times \dfrac{1}{1\%}$ Jonathan Frank, 3/21 Rye, NY |
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| 398168 (3.6) $11!\% - \dfrac{1}{1 \pmf}$ Jonathan Frank, 3/21 Rye, NY |
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| 399068 (3.6) $11!\% - \dfrac{1}{1 \%}$ Jonathan Frank, 3/21 Rye, NY |
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| 399157 (3.4) $11!\% - 11$ Jonathan Frank, 3/21 Rye, NY |
399158 (3.6) $11!\% - \dfrac{1}{.1}$ Jonathan Frank, 3/21 Rye, NY |
399159 (3.8) $11!\% - \dfrac{1}{.\overline{1}}$ Jonathan Frank, 3/21 Rye, NY |
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| 399165 (4.0) $11!\% - \sqrt{ \dfrac{1}{.\overline{1}}}$ Jonathan Frank, 3/21 Rye, NY |
399166 (3.4) $11!\% - 1 - 1$ Jonathan Frank, 3/21 Rye, NY |
399167 (3.4) $11!\% - 1 \times 1$ Jonathan Frank, 3/21 Rye, NY |
399168 (3.4) $11!\% \times 1 \times 1$ Jonathan Frank, 3/21 Rye, NY |
399169 (3.4) $11!\% + 1 \times 1$ Jonathan Frank, 3/21 Rye, NY |
399170 (3.4) $11!\% + 1 + 1$ Jonathan Frank, 3/21 Rye, NY |
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| 399171 (4.0) $11!\% + \sqrt{ \dfrac{1}{.\overline{1}}}$ Jonathan Frank, 3/21 Rye, NY |
399177 (3.8) $11!\% + \dfrac{1}{.\overline{1}}$ Jonathan Frank, 3/21 Rye, NY |
399178 (3.6) $11!\% + \dfrac{1}{.1}$ Jonathan Frank, 3/21 Rye, NY |
399179 (3.4) $11!\% + 11$ Jonathan Frank, 3/21 Rye, NY |
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| 399268 (3.6) $11!\% + \dfrac{1}{1 \%}$ Jonathan Frank, 3/21 Rye, NY |
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| 400168 (3.6) $11!\% + \dfrac{1}{1 \pmf}$ Jonathan Frank, 3/21 Rye, NY |
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| 492800 (4.0) $11! \times .\overline{1} \times .\overline{1}$ Jonathan Frank, 3/21 Rye, NY |
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| 531441 (4.6) $(-\log{(1 \pm)})^{11+1}$ Jonathan Frank, 3/21 Rye, NY |
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| 648000 (4.0) $\dfrac{((1 + 1 + 1)!)!}{.\overline{1}\%}$ Jonathan Frank, 3/21 Rye, NY |
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| 798336 (3.4) $11!\% \times (1 + 1)$ Jonathan Frank, 3/21 Rye, NY |
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| 945000 (5.8) $\left( \dfrac{1}{.\overline{1}} \right)!! \times \dfrac{1}{1 \pmf}$ Jonathan Frank, 3/21 Rye, NY |
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| 1000000 (3.4) $\dfrac{1}{1 \pmmf} + 1 - 1$ Jonathan Frank, 3/21 Rye, NY |
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| 1000002 (3.4) $\dfrac{1}{1 \pmmf} + 1 + 1$ Jonathan Frank, 3/21 Rye, NY |
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| 1039500 (5.4) $11!! \times \dfrac{1}{1\%}$ Jonathan Frank, 3/21 Rye, NY |
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| 1110000 (2.4) $\dfrac{111}{1\%\%}$ Jonathan Frank, 3/21 Rye, NY |
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| 1594323 (5.0) $(-\log{(1 \pm)})^{11-\log{(1\%)}}$ Jonathan Frank, 3/21 Rye, NY |
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| 3628799 (3.2) $(11 - 1)! - 1$ Jonathan Frank, 3/21 Rye, NY |
3628800 (3.2) $(11 - 1)! \times 1$ Jonathan Frank, 3/21 Rye, NY |
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| 3628801 (3.2) $(11 - 1)! + 1$ Jonathan Frank, 3/21 Rye, NY |
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| 3840000 (5.6) $\left( \dfrac{1}{.1} \right)!! \times \dfrac{1}{1 \pmf}$ Jonathan Frank, 3/21 Rye, NY |
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| 4194304 (4.6) $\left( \log \left( \dfrac{1}{1\%\%} \right)\right)^{11}$ Jonathan Frank, 3/21 Rye, NY |
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| 4782969 (5.0) $(-\log{(1 \pm)})^{11-\log{(1\pm)}}$ Jonathan Frank, 3/21 Rye, NY |
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| 10000000 (3.6) $\dfrac{1}{1\% \times 1 \pm \times 1\%}$ Jonathan Frank, 3/21 Rye, NY |
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| 10395000 (5.4) $11!! \times \dfrac{1}{1 \pmf}$ Jonathan Frank, 3/21 Rye, NY |
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| 39916789 (3.2) $11! - 11$ Jonathan Frank, 3/21 Rye, NY |
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| 39916798 (3.2) $11! - 1 - 1$ Jonathan Frank, 3/21 Rye, NY |
39916799 (3.2) $11! - 1 \times 1$ Jonathan Frank, 3/21 Rye, NY |
39916800 (3.2) $11! \times 1 \times 1$ Jonathan Frank, 3/21 Rye, NY |
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| 39916801 (3.2) $11! + 1 \times 1$ Jonathan Frank, 3/21 Rye, NY |
39916801 (3.2) $11! + 1 + 1$ Jonathan Frank, 3/21 Rye, NY |
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| 39916811 (3.2) $11! + 11$ Jonathan Frank, 3/21 Rye, NY |
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| 48828125 (4.6) $\left( \log \left( \dfrac{1}{1\% \pmf} \right)\right)^{11}$ Jonathan Frank, 3/21 Rye, NY |
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| 100000000 (3.4) $\left( \dfrac{1}{1\%\%} \right)^{1+1}$ Jonathan Frank, 3/21 Rye, NY |
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| 362797056 (4.6) $\left( \log \left( \dfrac{1}{1 \pmmf} \right)\right)^{11}$ Jonathan Frank, 3/21 Rye, NY |
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| 387420489 (4.2) $\left( \dfrac{1}{.\overline{1}} \right)^{1/.\overline{1}}$ Jonathan Frank, 3/21 Rye, NY |
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| 1000000000 (3.6) $\left( \dfrac{1}{.1} \right)^{1/.\overline{1}}$ Jonathan Frank, 3/21 Rye, NY |
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| 3486784401 (3.6) $(.\overline{1})^{-11+1}$ Jonathan Frank, 3/21 Rye, NY |
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| 10000000000 (3.4) $\left( \dfrac{1}{.1} \right)^{1/.1}$ Jonathan Frank, 3/21 Rye, NY |
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| 31381059609 (3.4) $\left( \dfrac{1}{.\overline{1}} \right)^{11}$ Jonathan Frank, 3/21 Rye, NY |
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| hundred billion (3.2) $\left( \dfrac{1}{.1} \right)^{11}$ Jonathan Frank, 3/21 Rye, NY |
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| 282429536481 (3.6) $(.\overline{1})^{-11-1}$ Jonathan Frank, 3/21 Rye, NY |
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| 285311670611 (3.0) $11^{11}$ Jonathan Frank, 3/21 Rye, NY |
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| trillion (3.4) $.1^{-11-1}$ Jonathan Frank, 3/21 Rye, NY |
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| ten trillion (4.6) $.1^{\log{(1\%)}-11}$ Jonathan Frank, 3/21 Rye, NY |
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| hundred trillion (4.6) $.1^{\log{(1\pm)}-11}$ Jonathan Frank, 3/21 Rye, NY |
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| quadrillion (3.6) $\sqrt[.1 + .1]{ \dfrac{1}{1 \pmf}}$ Jonathan Frank, 3/21 Rye, NY |
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| hundred quintillion (3.4) $\sqrt[.1]{ \dfrac{1}{1 \%}} \times 1$ Jonathan Frank, 3/21 Rye, NY |
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| ten sextillion (3.2) $\left( \dfrac{1}{1\%} \right)^{11}$ Jonathan Frank, 3/21 Rye, NY |
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| septillion (3.4) $(1 \%)^{-11-1}$ Jonathan Frank, 3/21 Rye, NY |
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| ten septillion (3.8) $\sqrt{\sqrt{ \left( \dfrac{1}{.1} \right)^{1/(1\%)}}}$ Jonathan Frank, 3/21 Rye, NY |
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| nonillion (3.2) $(1 \pm)^{1-11}$ Jonathan Frank, 3/21 Rye, NY |
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| decillion (3.2) $\left( \dfrac{1}{1 \pmf} \right)^{11}$ Jonathan Frank, 3/21 Rye, NY |
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| undecillion (3.4) $(1 \pm)^{-11-1}$ Jonathan Frank, 3/21 Rye, NY |
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| hundred tredecillion (3.4) $\left( \dfrac{1}{1\%\%} \right)^{11}$ Jonathan Frank, 3/21 Rye, NY |
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| hundred quinquadecillion (3.6) $\sqrt{ \left( \dfrac{1}{.1} \right)^{1/(1\%)}}$ Jonathan Frank, 3/21 Rye, NY |
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| ten septendecillion (3.4) $\left( \dfrac{1}{1\% \pmf} \right)^{11}$ Jonathan Frank, 3/21 Rye, NY |
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| unvigintillion (3.4) $\left( \dfrac{1}{1 \pmmf} \right)^{11}$ Jonathan Frank, 3/21 Rye, NY |
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| googol (2.4) $\left( \dfrac{1}{.1} \right)^{1/(1\%)}$ Paolo Pellegrini, 3/09 Martina Franca, Italy |
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| googolplex (3.8) $\left( \dfrac{1}{.1} \right) ^{\sqrt[-1\%]{.1}}$ Ralph Jeffords, 4/09 Centreville, VA |
PREVIOUS Page, Page 26 (10001+), ... Index to All Pages.