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There are 5281 feet in a mile and a foot. Create each of the positive integers using one copy of each of the digits 5, 2, 8, and 1, and any standard operations. All four numbers must be used, but no others. Your solutions will be assigned an exquisiteness level.
Computer analysis shows that if a set contains 4 digits, then the largest possible level 1 exquisiteness is achieved by the digits in the number 5281. Therefore, the name "Mile and a Foot" seems very appropriate, because this set will produce a very long sequence of level 1 solutions. This result suggested some additional questions.
Paolo Pellegrini has reported that the set {2, 3, 4, 22} produces an exquisiteness just one more than the exquisiteness of "Mile and a Foot". This result answers both questions above, but the questions can be rephrased for this new set. Does the set {2, 3, 4, 22} give the largest possible exquisiteness?
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 8 (2801+), ... Index to All Pages.
| 2805 (2.2) $\dfrac{28}{1\%} + 5$ Steve Wilson, 8/26 Lawrence, KS |
2808 (2.8) $\dfrac{\dfrac{5}{.8\%} - 1}{.\overline{2}}$ Steve Wilson, 8/26 Lawrence, KS |
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| 2815 (2.0) $2815$ Steve Wilson, 8/26 Lawrence, KS |
2817 (2.8) $\dfrac{\dfrac{5}{.8\%} + 1}{.\overline{2}}$ Steve Wilson, 8/26 Lawrence, KS |
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| 2825 (2.8) $\dfrac{25.\overline{1}}{.\overline{8}\%}$ Steve Wilson, 8/26 Lawrence, KS |
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| 2844 (2.8) $\dfrac{2 \times (8 - .1)}{.\overline{5}\%}$ Steve Wilson, 8/26 Lawrence, KS |
2850 (2.2) $\dfrac{285}{.1}$ Steve Wilson, 8/26 Lawrence, KS |
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| 2851 (2.0) $2851$ Steve Wilson, 8/26 Lawrence, KS |
2860 (2.6) $\dfrac{5.2}{.\overline{18}\%}$ Steve Wilson, 8/26 Lawrence, KS |
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| 2862 (2.8) $\dfrac{8 \times 2 - .1}{.\overline{5}\%}$ Steve Wilson, 8/26 Lawrence, KS |
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| 2872 (2.6) $8 \times \left(\dfrac{2}{.\overline{5}\%} - 1\right)$ Steve Wilson, 8/26 Lawrence, KS |
2875 (2.8) $\dfrac{\dfrac{2}{.\overline{1}} + 5}{.8\%}$ Steve Wilson, 8/26 Lawrence, KS |
2878 (2.6) $2 \times \left(\dfrac{8}{.\overline{5}\%} - 1\right)$ Steve Wilson, 8/26 Lawrence, KS |
2879 (2.6) $\dfrac{8 \times 2}{.\overline{5}\%} - 1$ Steve Wilson, 8/26 Lawrence, KS |
2880 (2.6) $\dfrac{8 \times 2}{.\overline{5}\%} \times 1$ Steve Wilson, 8/26 Lawrence, KS |
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| 2881 (2.6) $\dfrac{8 \times 2}{.\overline{5}\%} + 1$ Steve Wilson, 8/26 Lawrence, KS |
2882 (2.6) $2 \times \left(\dfrac{8}{.\overline{5}\%} + 1\right)$ Steve Wilson, 8/26 Lawrence, KS |
2888 (2.6) $8 \times \left(\dfrac{2}{.\overline{5}\%} + 1\right)$ Steve Wilson, 8/26 Lawrence, KS |
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| 2895 (2.4) $\dfrac{58 - .1}{2\%}$ Steve Wilson, 8/26 Lawrence, KS |
2898 (2.8) $\dfrac{8 \times 2 + .1}{.\overline{5}\%}$ Steve Wilson, 8/26 Lawrence, KS |
2899 (2.2) $\dfrac{58}{2\%} - 1$ Yi Zheng, 5/16 Olathe, KS |
2900 (2.2) $\dfrac{58}{2\%} \times 1$ Steve Wilson, 7/26 Lawrence, KS |
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| 2901 (2.2) $\dfrac{58}{2\%} + 1$ Yi Zheng, 5/16 Olathe, KS |
2905 (2.2) $\dfrac{581}{.2}$ Steve Wilson, 8/26 Lawrence, KS |
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| 3044 (3.4) $(.2)^{-5} - 81$ Jonathan Frank, 5/26 Piscataway, NJ |
3045 (3.6) $(.2)^{-5} - \dfrac{8}{.1}$ Steve Wilson, 7/26 Lawrence, KS |
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| 3072 (3.4) $(.5)^{-8} \times 12$ Jonathan Frank, 6/26 Piscataway, NJ |
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| 3107 (3.4) $(.2)^{-5} - 18$ Jonathan Frank, 5/26 Piscataway, NJ |
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| 3116 (3.4) $(.2)^{-5} - 8 - 1$ Jonathan Frank, 5/26 Piscataway, NJ |
3117 (3.4) $(.2)^{-5} - 8 \times 1$ Jonathan Frank, 5/26 Piscataway, NJ |
3118 (3.4) $(.2)^{-5} - 8 + 1$ Jonathan Frank, 5/26 Piscataway, NJ |
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| 3122 (3.4) $(.2)^{-5} - \sqrt{8 + 1}$ Steve Wilson, 7/26 Lawrence, KS |
3124 (2.4) $\dfrac{25}{.8\%} - 1$ Steve Wilson, 7/26 Lawrence, KS |
3125 (2.4) $\dfrac{25}{.8\%} \times 1$ Steve Wilson, 7/26 Lawrence, KS |
3126 (2.4) $\dfrac{25}{.8\%} + 1$ Steve Wilson, 7/26 Lawrence, KS |
3128 (3.4) $(.2)^{-5} + \sqrt{8 + 1}$ Steve Wilson, 7/26 Lawrence, KS |
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| 3132 (3.4) $(.2)^{-5} + 8 - 1$ Jonathan Frank, 5/26 Piscataway, NJ |
3133 (3.4) $(.2)^{-5} + 8 \times 1$ Jonathan Frank, 5/26 Piscataway, NJ |
3134 (3.4) $(.2)^{-5} + 8 + 1$ Jonathan Frank, 5/26 Piscataway, NJ |
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| 3143 (3.4) $(.2)^{-5} + 18$ Jonathan Frank, 5/26 Piscataway, NJ |
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| 3205 (3.6) $(.2)^{-5} + \dfrac{8}{.1}$ Steve Wilson, 7/26 Lawrence, KS |
3206 (3.4) $(.2)^{-5} + 81$ Jonathan Frank, 5/26 Piscataway, NJ |
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| 3264 (3.0) $8^2 \times 51$ Edward Gonzales, 12/10 Lawrence, KS |
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| 3363 (3.0) $58^2 - 1$ John Tader, 9/11 Olathe, KS |
3364 (3.0) $58^2 \times 1$ Steve Wilson, 7/26 Lawrence, KS |
3365 (3.0) $58^2 + 1$ Steve Wilson, 7/26 Lawrence, KS |
3370 (3.4) $\dfrac{8! + 5!}{12}$ Sean Collins, 3/10 Overland Park, KS |
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| 4000 (2.2) $\dfrac{8 \times 5}{(2 - 1)\%}$ Steve Wilson, 7/26 Lawrence, KS |
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| 4060 (2.0) $812 \times 5$ Edward Gonzales, 9/10 Lawrence, KS |
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| 4094 (3.0) $8^{5-1} - 2$ Steve Wilson, 8/26 Lawrence, KS |
4096 (2.0) $512 \times 8$ Steve Wilson, 5/26 Lawrence, KS |
4098 (3.0) $8^{5-1} + 2$ Steve Wilson, 8/26 Lawrence, KS |
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| 4105 (2.0) $821 \times 5$ Edward Gonzales, 9/10 Lawrence, KS |
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| 4168 (2.0) $521 \times 8$ Sean Collins, 3/10 Overland Park, KS |
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| 4182 (2.0) $82 \times 51$ Michele Gaston, 10/10 Olathe, KS |
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| 5376 (3.4) $(.5)^{-8} \times 21$ Jonathan Frank, 6/26 Piscataway, NJ |
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| 5800 (2.2) $\dfrac{58}{(2 - 1)\%}$ Steve Wilson, 7/26 Lawrence, KS |
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| 6250 (2.4) $\dfrac{5}{8\%\%} \times (2 - 1)$ Steve Wilson, 7/26 Lawrence, KS |
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| 7224 (3.0) $85^2 - 1$ Jonathan Frank, 4/26 Piscataway, NJ |
7225 (2.6) $\dfrac{8}{.\overline{1}\%} + 25$ Steve Wilson, 7/26 Lawrence, KS |
7226 (3.0) $85^2 + 1$ Michele Gaston, 10/10 Olathe, KS |
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| 7775 (3.0) $(8 - 2)^5 - 1$ Steve Wilson, 8/26 Lawrence, KS |
7776 (3.0) $(8 - 2)^{5 \times 1}$ Jonathan Frank, 4/26 Piscataway, NJ |
7777 (3.0) $(8 - 2)^5 + 1$ Steve Wilson, 8/26 Lawrence, KS |
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| 8000 (2.2) $8 \times 5 \times \dfrac{2}{1\%}$ Edward Gonzales, 10/10 Lawrence, KS |
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| 8192 (3.0) $8^{5-1} \times 2$ John Tader, 9/11 Olathe, KS |
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| 8500 (2.2) $\dfrac{85}{(2 - 1)\%}$ Steve Wilson, 7/26 Lawrence, KS |
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| 9600 (2.6) $\dfrac{\dfrac{1}{.5\%} - 8}{2\%}$ Steve Wilson, 7/26 Lawrence, KS |
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| 9995 (2.4) $\dfrac{8 + 2}{.1\%} - 5$ Steve Wilson, 7/26 Lawrence, KS |
10000 (2.4) $\dfrac{5 + 2 + 1}{8\%\%}$ Steve Wilson, 7/26 Lawrence, KS |
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| 10005 (2.4) $\dfrac{8 + 2}{.1\%} + 5$ Steve Wilson, 7/26 Lawrence, KS |
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| 11600 (2.2) $58 \times \dfrac{2}{1\%}$ Seth Musser, 11/10 Overland Park, KS |
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| 12500 (2.4) $\dfrac{2}{8\%} \times \dfrac{5}{1\%}$ Edward Gonzales, 10/10 Lawrence, KS |
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| 16383 (3.0) $\dfrac{8^5}{2} - 1$ Steve Wilson, 8/26 Lawrence, KS |
16384 (3.0) $2^{8 + 5 + 1}$ Jonathan Frank, 4/26 Piscataway, NJ |
16385 (3.0) $\dfrac{8^5}{2} + 1$ Steve Wilson, 8/26 Lawrence, KS |
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| 20808 (3.0) $51^2 \times 8$ Edward Gonzales, 11/10 Lawrence, KS |
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| 24964 (3.0) $158^2$ Joseph Geraci, 11/11 Leawood, KS |
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| 25000 (2.4) $\dfrac{1}{\left(2 - \dfrac85\right)\%\%}$ Steve Wilson, 8/26 Lawrence, KS |
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| 31104 (3.0) $\dfrac{12^5}{8}$ Ambra Robinson, 5/11 Lawrence, KS |
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| 32762 (3.2) $\sqrt[.2]{8} - 5 - 1$ Steve Wilson, 8/26 Lawrence, KS |
32763 (3.2) $\sqrt[.2]{8} - 5 \times 1$ Steve Wilson, 8/26 Lawrence, KS |
32764 (3.2) $\sqrt[.2]{8} - 5 + 1$ Steve Wilson, 8/26 Lawrence, KS |
32765 (3.0) $8^5 - 2 - 1$ Steve Wilson, 8/26 Lawrence, KS |
32766 (3.0) $8^5 - 2 \times 1$ Steve Wilson, 8/26 Lawrence, KS |
32767 (3.0) $8^5 - 2 + 1$ Steve Wilson, 8/26 Lawrence, KS |
32768 (3.0) $8^5 \times 1^2$ Steve Wilson, 8/26 Lawrence, KS |
32769 (3.0) $8^5 + 2 - 1$ Steve Wilson, 8/26 Lawrence, KS |
32770 (3.0) $8^5 + 2 \times 1$ Steve Wilson, 8/26 Lawrence, KS |
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| 32771 (3.0) $8^5 + 2 + 1$ Steve Wilson, 8/26 Lawrence, KS |
32772 (3.2) $\sqrt[.2]{8} + 5 - 1$ Steve Wilson, 8/26 Lawrence, KS |
32773 (3.2) $\sqrt[.2]{8} + 5 \times 1$ Steve Wilson, 8/26 Lawrence, KS |
32774 (3.2) $\sqrt[.2]{8} + 5 + 1$ Steve Wilson, 8/26 Lawrence, KS |
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| 46656 (3.0) $(8 - 2)^{5 + 1}$ Jonathan Frank, 4/26 Piscataway, NJ |
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| 50000 (2.4) $\dfrac{5 \times (8 + 2)}{.1\%}$ Steve Wilson, 8/26 Lawrence, KS |
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| 59047 (3.2) $\sqrt{81^5} - 2$ Chelsea Kiddle, 10/12 Leawood, KS |
59049 (3.0) $\sqrt[2]{81^5}$ Steve Wilson, 8/26 Lawrence, KS |
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| 59051 (3.2) $\sqrt{81^5} + 2$ Chelsea Kiddle, 10/12 Leawood, KS |
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| 65534 (3.0) $(5 - 1)^8 - 2$ Steve Wilson, 8/26 Lawrence, KS |
65536 (3.0) $8^5 \times 2 - 1$ Steve Wilson, 8/26 Lawrence, KS |
65536 (3.0) $8^5 \times 2 \times 1$ Steve Wilson, 8/26 Lawrence, KS |
65536 (3.0) $8^5 \times 2 + 1$ Steve Wilson, 8/26 Lawrence, KS |
65538 (3.0) $(5 - 1)^8 + 2$ Steve Wilson, 8/26 Lawrence, KS |
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| 99999 (3.0) $(8 + 2)^5 - 1$ Steve Wilson, 8/26 Lawrence, KS |
100000 (2.6) $\dfrac{5 + 2 + 1}{.8\%\%}$ Steve Wilson, 8/26 Lawrence, KS |
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| 100001 (3.0) $(2 + 8)^5 + 1$ Stephen Inglin, 9/09 DeSoto, KS |
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| 131072 (3.0) $\dfrac{8^{5 + 1}}{2}$ Steve Wilson, 8/26 Lawrence, KS |
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| 160000 (2.4) $\dfrac{8 \times (5 - 1)}{2\%}$ Steve Wilson, 8/26 Lawrence, KS |
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| 161051 (3.0) $(8 + 2 + 1)^5$ Mary Tuggle, 9/09 Kansas City, MO |
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| 248824 (3.0) $12^5 - 8$ Ambra Robinson, 2/11 Lawrence, KS |
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| 248840 (3.0) $12^5 + 8$ Ambra Robinson, 2/11 Lawrence, KS |
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| 262142 (3.0) $8^{5 + 1} - 2$ Steve Wilson, 8/26 Lawrence, KS |
262144 (3.0) $8^{5 + 2 - 1}$ Jonathan Frank, 4/26 Piscataway, NJ |
262146 (3.0) $8^{5 + 1} + 2$ Steve Wilson, 8/26 Lawrence, KS |
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| 295245 (3.4) $\dfrac{ \sqrt{81^5}}{.2}$ Seth Musser, 11/10 Overland Park, KS |
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| 390622 (3.0) $5^8 - 2 - 1$ Steve Wilson, 8/26 Lawrence, KS |
390623 (3.0) $5^8 - 2 \times 1$ Steve Wilson, 8/26 Lawrence, KS |
390624 (3.0) $5^8 - 2 + 1$ Steve Wilson, 8/26 Lawrence, KS |
390625 (2.6) $\dfrac{5}{12.8\%\%\%}$ Steve Wilson, 8/26 Lawrence, KS |
390626 (3.0) $5^8 + 2 - 1$ Steve Wilson, 8/26 Lawrence, KS |
390627 (3.0) $5^8 + 2 \times 1$ Joseph Geraci, 11/11 Leawood, KS |
390628 (3.0) $5^8 + 2 + 1$ Joseph Geraci, 11/11 Leawood, KS |
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| 393216 (3.0) $8^5 \times 12$ Edward Gonzales, 11/10 Lawrence, KS |
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| 604802 (3.2) $15 \times 8! + 2$ Obada Albadawi, 5/16 Overland Park, KS |
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| 688128 (3.0) $8^5 \times 21$ Edward Gonzales, 11/10 Lawrence, KS |
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| 781248 (3.0) $(5^8 - 1) \times 2$ Steve Wilson, 8/26 Lawrence, KS |
781249 (3.0) $5^8 \times 2 - 1$ Steve Wilson, 8/26 Lawrence, KS |
781250 (2.8) $\dfrac{1.5}{(2 - 8\%)\%\%\%}$ Steve Wilson, 8/26 Lawrence, KS |
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| 781251 (3.0) $5^8 \times 2 + 1$ Joseph Geraci, 11/11 Leawood, KS |
781252 (3.0) $(5^8 + 1) \times 2$ Steve Wilson, 8/26 Lawrence, KS |
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| 800000 (2.4) $\dfrac{8 \times 5 \times 2}{1\%\%}$ Steve Wilson, 8/26 Lawrence, KS |
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| 944784 (3.0) $\dfrac{18^5}{2}$ Ambra Robinson, 5/11 Lawrence, KS |
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| 1000000 (2.6) $\dfrac{5 + 2 + 1}{8\%\%\%}$ Steve Wilson, 8/26 Lawrence, KS |
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| 1048576 (3.4) $(.5)^{-18 - 2}$ Jonathan Frank, 7/26 Rye, NY |
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| 1889566 (3.0) $18^5 - 2$ Ambra Robinson, 5/11 Lawrence, KS |
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| 2097152 (3.0) $8^{2 + 5 \times 1}$ Jonathan Frank, 4/26 Piscataway, NJ |
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| 3779136 (3.0) $18^5 \times 2$ Edward Gonzales, 12/10 Lawrence, KS |
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| 8203125 (3.0) $5^8 \times 21$ Edward Gonzales, 11/10 Lawrence, KS |
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| 8388608 (3.0) $2^{15 + 8}$ Jonathan Frank, 7/26 Rye, NY |
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| 10000000 (3.0) $(5 \times 2)^{8 - 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 16777216 (3.0) $(5 + 2 + 1)^8$ Stephen Inglin, 9/09 DeSoto, KS |
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| 17210369 (3.0) $28^5 + 1$ Tyler Cox, 9/09 Olathe, KS |
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| 20643840 (3.2) $512 \times 8!$ Obada Albadawi, 5/16 Overland Park, KS |
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| 100000000 (3.0) $(5 \times 2)^{8 \times 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 134217728 (3.4) $(.5)^{-28 + 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 214990848 (3.2) $12^8 \times .5$ Chelsea Kiddle, 10/12 Leawood, KS |
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| 268435456 (3.4) $(.5)^{-28 \times 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 479001515 (3.2) $12! - 85$ Obada Albadawi, 5/16 Overland Park, KS |
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| 479001685 (3.2) $12! + 85$ Obada Albadawi, 5/16 Overland Park, KS |
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| 536870912 (3.4) $(.5)^{-28 - 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 1000000000 (3.0) $(5 \times 2)^{8 + 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 1073741824 (3.0) $8^{5 \times 2 \times 1}$ Jonathan Frank, 8/26 Rye, NY |
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| 2149908480 (3.0) $12^8 \times 5$ Edward Gonzales, 11/10 Lawrence, KS |
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| 3707398432 (3.0) $82^5 \times 1$ Edward Gonzales, 12/10 Lawrence, KS |
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| 4294967296 (3.0) $2^{(5 - 1) \times 8}$ Jonathan Frank, 7/26 Rye, NY |
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| 8589934592 (3.0) $8^{5 \times 2 + 1}$ Jonathan Frank, 8/26 Rye, NY |
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| 34359738368 (3.0) $128^5$ Jessie Shore, 1/11 Lawrence, KS |
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| 68719476736 (3.4) $(.5)^{-18 \times 2}$ Jonathan Frank, 7/26 Rye, NY |
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| 549755813888 (3.0) $2^{8 \times 5 - 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 1099511627776 (3.0) $2^{8 \times 5 \times 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 2199023255552 (3.0) $2^{8 \times 5 + 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 35184372088832 (3.0) $2^{(8 + 1) \times 5}$ Jonathan Frank, 7/26 Rye, NY |
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| 281474976710656 (3.0) $2^{(5 + 1) \times 8}$ Jonathan Frank, 7/26 Rye, NY |
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| 2251799813685248 (3.0) $8^{15 + 2}$ Jonathan Frank, 8/26 Rye, NY |
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| 72057594037927936 (3.0) $(5 - 1)^{28}$ Jonathan Frank, 8/26 Rye, NY |
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| 144115188075855872 (3.0) $2^{58 - 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 288230376151711744 (3.0) $2^{58 \times 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 576460752303423488 (3.0) $2^{58 + 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 1000000000000000000 (3.0) $(5 \times 2)^{18}$ Jonathan Frank, 7/26 Rye, NY |
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| 100000000000000000000 (3.4) $(.1^{-5})^{8/2}$ Jonathan Frank, 7/26 Rye, NY |
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| 4722366482869645213696 (3.0) $8^{25 - 1}$ Jonathan Frank, 8/26 Rye, NY |
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| 37778931862957161709568 (3.0) $8^{25 \times 1}$ Jonathan Frank, 8/26 Rye, NY |
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| 75557863725914323419136 (3.0) $2^{81 - 5}$ Jonathan Frank, 7/26 Rye, NY |
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| 302231454903657293676544 (3.0) $8^{25 + 1}$ Jonathan Frank, 8/26 Rye, NY |
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| 604462909807314587353088 (3.4) $(.5)^{-81 + 2}$ Jonathan Frank, 7/26 Rye, NY |
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| 1000000000000000000000000 (3.4) $(.1^{-8})^{5-2}$ Jonathan Frank, 7/26 Rye, NY |
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| 2417851639229258349412352 (3.4) $(.5)^{-82 + 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 4835703278458516698824704 (3.4) $(.5)^{-82 \times 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 9671406556917033397649408 (3.4) $(.5)^{-82 - 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 19342813113834066795298816 (3.0) $2^{85 - 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 38685626227668133590597632 (3.0) $2^{85 \times 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 77371252455336267181195264 (3.0) $2^{85 + 1}$ Jonathan Frank, 7/26 Rye, NY |
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| 100000000000000000000000000 (3.4) $(.1^{-2})^{8 + 5}$ Jonathan Frank, 7/26 Rye, NY |
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| 1237940039285380274899124224 (3.0) $2^{18 \times 5}$ Jonathan Frank, 7/26 Rye, NY |
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| 1000000000000000000000000000000 (3.4) $(.1^{-5})^{8-2}$ Jonathan Frank, 7/26 Rye, NY |
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| 1329227995784915872903807060280344576 (3.0) $2^{15 \times 8}$ Jonathan Frank, 7/26 Rye, NY |
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| 340282366920938463463374607431768211456 (3.4) $(.5)^{-128}$ Jonathan Frank, 7/26 Rye, NY |
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| hundred septendecillion (3.4) $(.1^{-8})^{5+2}$ Jonathan Frank, 7/26 Rye, NY |
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| hundred quinquavigintillion (3.4) $(.1^{-2})^{5 \times 8}$ Jonathan Frank, 7/26 Rye, NY |
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| sesvigintillion (3.0) $(5 \times 2)^{81}$ Jonathan Frank, 7/26 Rye, NY |
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| googol (3.6) $.1 ^{-\sqrt[.5]{2+8}}$ Ralph Jeffords, 10/09 Centreville, VA |
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| hundred septentrigintillion (3.4) $(.1^{-2})^{58}$ Jonathan Frank, 7/26 Rye, NY |
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| hundred quinquaquadragintillion (3.4) $(.1^{-5})^{28}$ Jonathan Frank, 7/26 Rye, NY |
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| hundred quinquaquinquagintillion (3.4) $(.1^{-2})^{85}$ Jonathan Frank, 7/26 Rye, NY |
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| hundred quinquasexagintillion (3.4) $(.1^{-8})^{25}$ Jonathan Frank, 7/26 Rye, NY |
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| hundred quinquatrigintacentillion (3.4) $(.1^{-5})^{82}$ Jonathan Frank, 7/26 Rye, NY |
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| hundred septentrigintacentillion (3.4) $(.1^{-8})^{52}$ Jonathan Frank, 7/26 Rye, NY |
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| novenquinquagintacentillion (3.6) $(.1^{-8})^{5!/2}$ Jonathan Frank, 7/26 Rye, NY |
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| tresvigintiducentillion (3.8) $(.1^{-2})^{8!/5!}$ Jonathan Frank, 7/26 Rye, NY |
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| hundred tredecitrecentillion (3.6) $(.1^{-8})^{5!-2}$ Jonathan Frank, 7/26 Rye, NY |
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| ten quattuorvigintitrecentillion (3.6) $(.1^{-8})^{5!+2}$ Jonathan Frank, 7/26 Rye, NY |
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| googolplex (3.8) $(2+8) ^{ \sqrt[-5\%]{1\% ‰}}$ Ralph Jeffords, 10/09 Centreville, VA |
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