$\def\pm{{ ‰}} \def\pmf{{ ‰ \phantom.}} \def\pmm{{ ‰ \! ‰}} \def\pmmf{{ ‰ \! ‰ \phantom\%}}$

## Integermania!

#### Digits of Pi

This Integermania problem is a bit different than the others, as different digits will be used to create each of the integers. In particular, the following two ADDITIONAL rules must be met:

• To create the integer $N$, you must use the five digits that appear from the $(5N-4)$th to $(5N)$th place of the decimal expansion of $\pi$.
• The digits used to create $N$ must be in the same order as they occur in the decimal expansion of $\pi$.
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.

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 0 (1.0) $0 + 0 + 0 + 0 \times 3.$ Steve Wilson, 3/23Lawrence, KS 1 (1.0) $\dfrac{1 \times 4 + 1 \times 5}{9}$ Steve Wilson, 3/23Lawrence, KS 2 (1.0) $\dfrac{2 \times 6 - 5 + 3}{5}$ Dana Reigle, 3/23Lewisburg, PA 3 (1.0) $(8 + 9 - 7 - 9) \times 3$ Dana Reigle, 3/23Lewisburg, PA 4 (1.0) $2 \times 3 + 8 - 4 - 6$ Dana Reigle, 3/23Lewisburg, PA 5 (1.0) $2 - (6 - 4 - 3) \times 3$ Dana Reigle, 3/23Lewisburg, PA 6 (1.0) $(8 + 3) \times 2 - 7 - 9$ Dana Reigle, 3/23Lewisburg, PA 7 (1.0) $5 + 0 + 2 + 8 - 8$ Steve Wilson, 3/23Lawrence, KS 8 (1.0) $4 + 1 + 9 - 7 + 1$ Steve Wilson, 3/23Lawrence, KS 9 (1.0) $6 + \dfrac93 + 9 - 9$ Steve Wilson, 3/23Lawrence, KS 10 (1.0) $(3 + 7) + (5 + 1) \times 0$ Jacob Heasley, 3/23York, PA 11 (1.0) $\dfrac{5 \times 8}{2} + 0 - 9$ Jacob Heasley, 3/23York, PA 12 (1.0) $7 + 4 + 9 - 4 - 4$ Jacob Heasley, 3/23York, PA 13 (1.0) $5 + 9 + 2 - 3 + 0$ Jacob Heasley, 3/23York, PA 14 (1.0) $\dfrac{7}{8 \times 1 - 6} \times 4$ Jacob Heasley, 3/23York, PA 15 (2.2) $0 + \dfrac{6}{.2 \times (8 - 6)}$ Steve Wilson, 4/23Lawrence, KS 16 (1.0) $(2 + 0) \times 8 + 9 - 9$ Dana Reigle, 4/23Lewisburg, PA 17 (2.4) $8 + \dfrac{6 + 2}{.\overline{8}} + 0$ Steve Wilson, 4/23Lawrence, KS 18 (1.0) $3 + 4 + 8 - 2 + 5$ Dana Reigle, 4/23Lewisburg, PA 19 (1.0) $3 \times (4 + 2) \times 1 + 1$ Dana Reigle, 4/23Lewisburg, PA 20 (2.4) $(7 + 0 + 6 + 7) \times .\overline{9}$ Steve Wilson, 4/23Lawrence, KS 21 (1.0) $8 \times 2 + 1 - 4 + 8$ Dana Reigle, 4/23Lewisburg, PA 22 (1.0) $0 - 8 + 6 \times 5 \times 1$ Steve Wilson, 4/23Lawrence, KS 23 (1.0) $(3 + 2) \times \dfrac82 + 3$ Dana Reigle, 4/23Lewisburg, PA 24 (1.0) $0 + 6 - 6 \times (4 - 7)$ Dana Reigle, 5/23Lewisburg, PA 25 (1.0) $0 + 9 \times 3 - \dfrac84$ Dana Reigle, 5/23Lewisburg, PA 26 (1.2) $-4 + 6 \times (0 \times 9 + 5)$ Dana Reigle, 5/23Lewisburg, PA 27 (2.0) $(5 + 0) \times 5.8 - 2$ Steve Wilson, 5/23Lawrence, KS 28 (1.0) $2 + (3 + 1) \times 7 - 2$ Dana Reigle, 5/23Lewisburg, PA 29 (1.2) $- 5 + 3 - 5 + 9 \times 4$ Dana Reigle, 5/23Lewisburg, PA 30 (2.2) $0 + 8 \times \dfrac{1 + 2}{.8}$ Steve Wilson, 5/23Lawrence, KS 31 (1.0) $4 \times 8 - 1 \times 1 \times 1$ Steve Wilson, 5/23Lawrence, KS 32 (1.0) $(7 + 4 + 5) \times (0 + 2)$ Steve Wilson, 5/23Lawrence, KS 33 (1.0) $8 \times 4 + 1 + 0 \times 2$ Steve Wilson, 5/23Lawrence, KS 34 (1.0) $7 + 0 + 1 \times 9 \times 3$ Dana Reigle, 6/23Lewisburg, PA 35 (2.0) $8 \times (5 - 2) + 11$ Dana Reigle, 6/23Lewisburg, PA 36 (1.0) $0 + \left(5 - \dfrac55\right) \times 9$ Steve Wilson, 6/23Lawrence, KS 37 (2.0) $\dfrac{64 + 4 + 6}{2}$ Dana Reigle, 6/23Lewisburg, PA 38 (1.0) $2 - 9 \times 4 \times (8 - 9)$ Dana Reigle, 6/23Lewisburg, PA 39 (2.0) $(5 - 4) \times 9 + 30$ Dana Reigle, 6/23Lewisburg, PA 40 (1.0) $3 \times 8 + 1 + 9 + 6$ Steve Wilson, 6/23Lawrence, KS 41 (2.0) $44 - 2 - \dfrac88$ Steve Wilson, 6/23Lawrence, KS 42 (2.2) $10 + \dfrac{9 + 7}{.5}$ Steve Wilson, 6/23Lawrence, KS 43 (1.0) $6 \times 6 - 5 + 9 + 3$ Steve Wilson, 6/23Lawrence, KS 44 (2.0) $34 + 4 + 6 \times 1$ Dana Reigle, 7/23Lewisburg, PA 45 (1.2) $(-2 + 8 - 4 + 7) \times 5$ Dana Reigle, 7/23Lewisburg, PA 46 (1.2) $-6 + 4 + 8 \times 2 \times 3$ Steve Wilson, 10/23Lawrence, KS 47 (2.4) $.\overline{3} \times (7 + 8) + 6 \times 7$ Steve Wilson, 7/23Lawrence, KS 48 (1.0) $8 \times 3 \times (1 + 6 - 5)$ Dana Reigle, 7/23Lewisburg, PA 49 (2.2) $-2 + 71 - 20$ Steve Wilson, 7/23Lawrence, KS 50 (2.6) $\dfrac{1 + 9}{.0\overline{9} + .1}$ Steve Wilson, 7/23Lawrence, KS 51 (2.0) $45 - 6 + 4 + 8$ Steve Wilson, 7/23Lawrence, KS 52 (1.0) $5 + 6 \times 6 + 9 + 2$ Dana Reigle, 7/23Lewisburg, PA 53 (3.2) $3 + 46 + 0! + 3$ Steve Wilson, 9/23Lawrence, KS 54 (2.0) $48 + 6 + 1 \times 0$ Steve Wilson, 7/23Lawrence, KS 55 (2.0) $45 + 4 \times 3 - 2$ Dana Reigle, 8/23Lewisburg, PA 56 (1.0) $6 \times 6 + 4 + 8 \times 2$ Dana Reigle, 8/23Lewisburg, PA 57 (1.0) $(1 + 3 \times 3 + 9) \times 3$ Steve Wilson, 8/23Lawrence, KS 58 (3.2) $-6 + 0 \times 7 + 2^6$ Steve Wilson, 9/23Lawrence, KS 59 (2.2) $0 + \dfrac{2}{4\%} + 9 \times 1$ Steve Wilson, 8/23Lawrence, KS 60 (1.0) $(4 \times 1 + 2) \times (7 + 3)$ Steve Wilson, 8/23Lawrence, KS 61 (2.8) $-.7 - 2 \times .4 + \dfrac{5}{8\%}$ Steve Wilson, 9/23Lawrence, KS 62 (3.6) $70 + 0! - \dfrac{6}{.\overline{6}}$ Steve Wilson, 10/23Lawrence, KS 63 (3.0) $0 + 63 \times 1^5$ Steve Wilson, 9/23Lawrence, KS 64 (2.2) $.5 \times (8 + 8) \times (1 + 7)$ Steve Wilson, 9/23Lawrence, KS 65 (2.2) $\left( 4 + \dfrac{8}{.8} - 1 \right) \times 5$ Steve Wilson, 10/23Lawrence, KS 66 (3.4) $(2 + 0!)! \times (9 + 2 + 0)$ Steve Wilson, 10/23Lawrence, KS 67 (1.0) $9 + 6 \times (2 + 8) - 2$ Dana Reigle, 8/23Lewisburg, PA 68 (2.8) $\left( .\overline{9} + .2 + .5 \right) \times 40$ Steve Wilson, 10/23Lawrence, KS 69 (2.0) $91 - 7 - 15$ Dana Reigle, 8/23Lewisburg, PA 70 (2.0) $3 + 64 - 3 + 6$ Dana Reigle, 8/23Lewisburg, PA 71 (2.0) $7 + 89 - 25$ Dana Reigle, 10/23Lewisburg, PA 72 (1.0) $(9 + 0 + 3) \times (6 + 0)$ Steve Wilson, 11/23Lawrence, KS 73 (3.2) $0 + 1 + (1 + 3)! \times 3$ Dana Reigle, 10/23Lewisburg, PA 74 (3.4) $-0! + 5 \times 3 \times (0 + 5)$ Steve Wilson, 11/23Lawrence, KS 75 (2.2) $\dfrac{4 + 8}{8 \times 2\%} + 0$ Steve Wilson, 11/23Lawrence, KS 76 (1.0) $4 \times (6 + 6 + 5 + 2)$ Dana Reigle, 9/23Lewisburg, PA 77 (3.2) $(1 + 3!) \times (8 + 4 - 1)$ Dana Reigle, 10/23Lewisburg, PA 78 (1.0) $4 \times 6 + 9 \times (5 + 1)$ Steve Wilson, 11/23Lawrence, KS 79 (2.0) $94 - 15 \times 1$ Dana Reigle, 9/23Lewisburg, PA 80 (2.0) $16 \times (0 + 9 - 4)$ Dana Reigle, 10/23Lewisburg, PA 81 (3.0) $(3 \times 3)^{0 - 5 + 7}$ Steve Wilson, 11/23Lawrence, KS 82 (2.2) $(2 \times 7 - 0.\overline{3}) \times 6$ Steve Wilson, 12/23Lawrence, KS 83 (2.4) $-5 \times 7 + \dfrac{59}{.5}$ Steve Wilson, 12/23Lawrence, KS 84 (2.0) $91 - 9 + 5 - 3$ Dana Reigle, 11/23Lewisburg, PA 85 (2.0) $0 + 92 + 1 - 8$ Dana Reigle, 11/23Lewisburg, PA 86 (2.0) $6 + 11 \times 7 + 3$ Steve Wilson, 12/23Lawrence, KS 87 (1.0) $(8 + 1) \times 9 + 3 \times 2$ Dana Reigle, 11/23Lewisburg, PA 88 (3.6) $6 + \sqrt{\dfrac{1}{.\overline{1}}} + 79$ Steve Wilson, 12/23Lawrence, KS 89 (3.4) $-31 + 0 + 5! \times 1$ Dana Reigle, 11/23Lewisburg, PA 90 (1.0) $(1 + 8) \times \dfrac{5}{4/8}$ Dana Reigle, 11/23Lewisburg, PA 91 (3.2) $0! + (7 + 4 + 4) \times 6$ Steve Wilson, 12/23Lawrence, KS 92 (2.0) $(2 - 3) \times 7 + 99$ Dana Reigle, 12/23Prague, Czech Republic 93 (3.2) $62 + 7 \times 4 + \sqrt{9}$ Steve Wilson, 1/24Lawrence, KS 94 (1.2) $-5 - 6 + 7 \times 3 \times 5$ Dana Reigle, 12/23Prague, Czech Republic 95 (3.2) $-1^8 + 8 \times (5 + 7)$ Steve Wilson, 1/24Lawrence, KS 96 (3.2) $(5 + 2) \times 7 \times 2 - \sqrt{4}$ Steve Wilson, 1/24Lawrence, KS 97 (3.2) $8 + 91 - \sqrt{2 \times 2}$ Steve Wilson, 1/24Lawrence, KS 98 (3.4) $7 + \dfrac{\sqrt{9}}{.3} + 81$ Steve Wilson, 1/24Lawrence, KS 99 (3.0) $(8 + 3^0) \times 11$ Dana Reigle, 1/24Lewisburg, PA 100 (2.0) $94 + 9 - 1 - 2$ Dana Reigle, 12/23Prague, Czech Republic 101 (2.0) $98 + 3 \times 3 - 6$ Steve Wilson, 2/24Lawrence, KS 102 (2.0) $7 + 33 + 62$ Steve Wilson, 2/24Lawrence, KS 103 (2.2) $\dfrac{4}{4\%} + 0.6 \times 5$ Steve Wilson, 3/24Lawrence, KS 104 (2.2) $\dfrac{6}{6\%} + 4 + 3 \times 0$ Steve Wilson, 2/24Lawrence, KS 105 (3.4) $86 - 0! + \dfrac{2}{.1}$ Steve Wilson, 2/24Lawrence, KS 106 (3.8) $3! + (.\overline{9} + 49) \times \sqrt{4}$ Steve Wilson, 2/24Lawrence, KS 107 (1.2) $(-6 + 3 \times 9) \times 5 + 2$ Dana Reigle, 2/24Lewisburg, PA 108 (3.0) $2^4 \times 7 + 3 - 7$ Dana Reigle, 1/24Lewisburg, PA 109 (3.6) $1 \times 9 + \dfrac{0!^7}{0!\%}$ Steve Wilson, 3/24Lawrence, KS 110 (2.2) $2 \times (-1 + 7) + 98$ Dana Reigle, 2/24Lewisburg, PA 111 (3.0) $(6^0 + 9 \times 4) \times 3$ Dana Reigle, 2/24Lewisburg, PA 112 (1.0) $7 \times (0 + 2 + 7 + 7)$ Dana Reigle, 2/24Lewisburg, PA 113 (3.4) $0 + 5! - 3 \times \sqrt{9} + 2$ Steve Wilson, 3/24Lawrence, KS 114 (2.0) $1 + 7 \times 17 - 6$ Dana Reigle, 2/24Lewisburg, PA 115 (3.2) $2 \times 9 \times 3! + 1 \times 7$ Steve Wilson, 3/24Lawrence, KS 116 (2.2) $-6 + 7 + 5 \times 23$ Steve Wilson, 3/24Lawrence, KS 117 (3.6) $\dfrac{84}{.\overline{6}} - 7 - \sqrt{4}$ Steve Wilson, 4/24Lawrence, KS 118 (2.0) $(8 + 1) \times 8 + 46$ Dana Reigle, 3/24Lewisburg, PA 119 (1.0) $7 + (6 + 6) \times 9 + 4$ Dana Reigle, 3/24Lewisburg, PA 120 (3.2) $0 + 5! \times 1 \times (3 - 2)$ Steve Wilson, 4/24Lawrence, KS 121 (3.6) $0! + 0 + \dfrac{(0! + 5)!}{6}$ Steve Wilson, 4/24Lawrence, KS 122 (3.6) $\sqrt{8 + 1} + (-2 + 7)! - 1$ Steve Wilson, 4/24Lawrence, KS 123 (2.0) $45 + 26 \times 3$ Steve Wilson, 4/24Lawrence, KS 56082 77857 71342 75778 96091 73637 17872 14684 40901 22495 34301 46549 58537 10507 92279 68925 89235

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