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

## Integermania!

#### Four Fours

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.

 1 (1.0) $\dfrac{4+4}{4+4}$ Carolyn Neptune, 3/06Prairie Village, KS 2 (1.0) $\dfrac{4 \times 4}{4 + 4}$ Carolyn Neptune, 4/06Prairie Village, KS 3 (1.0) $\dfrac{4 \times 4 - 4}{4}$ Dave Jones, 5/06Coventry, England 4 (1.0) $(4 - 4) \times 4 + 4$ Dave Jones, 5/06Coventry, England 5 (1.0) $\dfrac{4 \times 4 + 4}{4}$ Dave Jones, 5/06Coventry, England 6 (1.0) $4 + \dfrac{4+4}{4}$ Dave Jones, 5/06Coventry, England 7 (1.0) $4 + 4 - \dfrac44$ Dave Jones, 5/06Coventry, England 8 (1.0) $4 \times 4 - 4 - 4$ Christie Birzer, 3/06Shawnee, KS 9 (1.0) $4 + 4 + \dfrac44$ Dave Jones, 4/06Coventry, England 10 (2.0) $\dfrac{44 - 4}{4}$ Christie Birzer, 3/06Shawnee, KS 11 (2.2) $\dfrac{4}{.4} + \dfrac44$ Matt Watters, 4/06Prairie Village, KS 12 (1.0) $4 \times \left( 4 - \dfrac44 \right)$ Levi Self, 6/06San Antonio, TX 13 (2.4) $\dfrac{4}{.\overline{44}} + 4$ Steve Wilson, 7/06Raytown, MO 14 (2.4) $\dfrac{4+4}{.\overline{4}} - 4$ Steve Wilson, 7/06Raytown, MO 15 (1.0) $4 \times 4 - \dfrac44$ Dave Jones, 4/06Coventry, England 16 (1.0) $4 \times 4 \times \dfrac44$ Dave Jones, 4/06Coventry, England 17 (1.0) $4 \times 4 + \dfrac44$ Dave Jones, 4/06Coventry, England 18 (2.2) $\dfrac{4}{.4} + 4 + 4$ Steve Wilson, 7/06Raytown, MO 19 (2.4) $\dfrac{4 + 4 - .4}{.4}$ Dave Jones, 1/07Coventry, England 20 (1.0) $4 \times \left( 4 + \dfrac44 \right)$ Dave Jones, 4/06Coventry, England 21 (2.2) $\dfrac{4}{4 \times 4\%} - 4$ Dave Jones, 10/06Coventry, England 22 (2.4) $\dfrac{4 + 4}{.\overline{4}} + 4$ Steve Wilson, 7/06Raytown, MO 23 (3.2) $4! - 4^{4-4}$ Paolo Pellegrini, 7/08Martina Franca, Italy 24 (1.0) $4 \times 4 + 4 + 4$ Carolyn Neptune, 4/06Prairie Village, KS 25 (2.4) $4 \times 4 + \dfrac{4}{.\overline{4}}$ Dave Jones, 1/07Coventry, England 26 (2.2) $4 \times 4 + \dfrac{4}{.4}$ Dave Jones, 10/06Coventry, England 27 (2.4) $\dfrac{4 + 4 + 4}{.\overline{4}}$ Dave Jones, 1/07Coventry, England 28 (1.0) $4 \times (4 + 4) - 4$ Steve Wilson, 5/06Raytown, MO 29 (2.2) $\dfrac{4}{4 \times 4\%} + 4$ Dave Jones, 10/06Coventry, England 30 (2.2) $\dfrac{4 + 4 + 4}{.4}$ Steve Wilson, 6/06Raytown, MO 31 (3.2) $\sqrt[.4]{4} - \dfrac44$ Paolo Pellegrini, 7/08Martina Franca, Italy 32 (1.0) $4 \times 4 + 4 \times 4$ Levi Self, 6/06San Antonio, TX 33 (3.2) $\sqrt[.4]{4} + \dfrac44$ Paolo Pellegrini, 7/08Martina Franca, Italy 34 (2.2) $44 -\dfrac{4}{.4}$ Dave Jones, 6/06Coventry, England 35 (2.4) $44 - \dfrac{4}{.\overline{4}}$ Steve Wilson, 8/06Raytown, MO 36 (1.0) $(4 + 4) \times 4 + 4$ Levi Self, 6/06San Antonio, TX 37 (2.8) $\dfrac{4 \times 4 + .\overline{4}}{.\overline{4}}$ Dave Jones, 4/07Coventry, England 38 (3.2) $44 - \dfrac{4!}{4}$ Steve Wilson, 10/08Raytown, MO 39 (2.4) $\dfrac{4 \times 4 - .4}{.4}$ Dave Jones, 1/07Coventry, England 40 (2.4) $4 \times \dfrac{4}{.\overline{4}} + 4$ Steve Wilson, 6/06Raytown, MO 41 (2.4) $\dfrac{4 \times 4 + .4}{.4}$ Dave Jones, 1/07Coventry, England 42 (3.2) $44 - 4 + \sqrt{4}$ Steve Wilson, 8/06Raytown, MO 43 (2.0) $44 - \dfrac44$ Carolyn Neptune, 5/06Prairie Village, KS 44 (2.0) $44 \times \dfrac44$ Carolyn Neptune, 5/06Prairie Village, KS 45 (2.0) $44 + \dfrac44$ Carolyn Neptune, 5/06Prairie Village, KS 46 (2.2) $\dfrac{4}{(4+4)\%} - 4$ Steve Wilson, 1/07Raytown, MO 47 (3.4) $4! + 4! - \dfrac44$ Steve Wilson, 10/06Raytown, MO 48 (1.0) $(4 \times 4 - 4) \times 4$ Steve Wilson, 5/06Raytown, MO 49 (3.2) $\dfrac{.4}{(.\overline{4} + .\overline{4})\%} + 4$ Steve Wilson, 10/08Raytown, MO 50 (2.2) $\dfrac{4 \times 4 + 4}{.4}$ Steve Wilson, 6/06Raytown, MO 51 (3.4) $\dfrac{\sqrt{4}}{4\%} + \dfrac44$ Paolo Pellegrini, 7/08Martina Franca, Italy 52 (2.0) $44 + 4 + 4$ Carolyn Neptune, 5/06Prairie Village, KS 53 (2.4) $44 + \dfrac{4}{.\overline{4}}$ Steve Wilson, 8/06Raytown, MO 54 (2.2) $44 + \dfrac{4}{.4}$ Dave Jones, 6/06Coventry, England 55 (2.2) $\dfrac{4.4}{(4 + 4)\%}$ Steve Wilson, 10/08Raytown, MO 56 (2.2) $\dfrac{4}{4\%} - 44$ Steve Wilson, 8/06Raytown, MO 57 (3.6) $\dfrac{4! + .4}{.4} - 4$ Paolo Pellegrini, 7/08Martina Franca, Italy 58 (3.2) $\dfrac{4^4 - 4!}{4}$ Steve Wilson, 10/08Raytown, MO 59 (3.4) $\dfrac{4!}{.4} - \dfrac44$ Ralph Jeffords, 2/07Centreville, VA 60 (1.0) $4 \times 4 \times 4 - 4$ Steve Wilson, 5/06Raytown, MO 61 (3.4) $\dfrac{4!}{.4} + \dfrac44$ Steve Wilson, 3/06Raytown, MO 62 (3.2) $4 \times 4 \times 4 - \sqrt{4}$ Carolyn Neptune, 10/06Prairie Village, KS 63 (3.0) $\dfrac{4^4 - 4}{4}$ Steve Wilson, 11/06Raytown, MO 64 (1.0) $(4 + 4) \times (4 + 4)$ Steve Wilson, 5/06Raytown, MO 65 (3.0) $\dfrac{4^4 + 4}{4}$ Steve Wilson, 11/06Raytown, MO 66 (3.2) $4 \times 4 \times 4 + \sqrt{4}$ Carolyn Neptune, 10/06Prairie Village, KS 67 (3.6) $\dfrac{4! + 4}{.\overline{4}} + 4$ Ralph Jeffords, 3/07Centreville, VA 68 (1.0) $4 \times 4 \times 4 + 4$ Steve Wilson, 5/06Raytown, MO 69 (3.6) $\dfrac{4! + \sqrt{4}}{.4} + 4$ Steve Wilson, 12/06Raytown, MO 70 (3.2) $\dfrac{4^4 + 4!}{4}$ Steve Wilson, 10/08Raytown, MO 71 (3.4) $\dfrac{4! + 4.4}{.4}$ Steve Wilson, 3/06Raytown, MO 72 (2.4) $(4 + 4) \times \dfrac{4}{.\overline{4}}$ Steve Wilson, 9/06Raytown, MO 73 (3.8) $\dfrac{\sqrt{4} - 4\%}{4\%} + 4!$ Steve Wilson, 12/07Raytown, MO 74 (2.8) $\dfrac{.4}{.\overline{4}\%} - 4 \times 4$ Steve Wilson, 9/06Raytown, MO 75 (2.2) $\dfrac{4 - \dfrac44}{4\%}$ Dave Jones, 11/06Coventry, England 76 (3.2) $4 \times (4! - 4) - 4$ Steve Wilson, 10/08Raytown, MO 77 (3.0) $\dfrac{.4 - 4\%}{.\overline{4}\%} - 4$ Steve Wilson, 2/07Raytown, MO 78 (3.4) $(4! - 4) \times 4 - \sqrt{4}$ Steve Wilson, 11/06Raytown, MO 79 (3.6) $\dfrac{ \sqrt[.4]{4} - .4}{.4}$ Paolo Pellegrini, 7/08Martina Franca, Italy 80 (1.0) $(4 \times 4 + 4) \times 4$ Levi Self, 6/06San Antonio, TX 81 (2.6) $\dfrac{4 - .4}{4.\overline{4}\%}$ Dave Jones, 2/07Coventry, England 82 (2.8) $\dfrac{.4}{.\overline{4}\%} - 4 - 4$ Steve Wilson, 9/06Raytown, MO 83 (3.8) $\sqrt{ \left( \dfrac{4}{.\overline{4}} \right)^4} + \sqrt{4}$ Ralph Jeffords, 12/06Centreville, VA 84 (2.2) $\dfrac{4}{4\%} - 4 \times 4$ Dave Jones, 10/06Coventry, England 85 (3.0) $\dfrac{.4 - 4\%}{.\overline{4}\%} + 4$ Steve Wilson, 2/07Raytown, MO 86 (2.4) $\dfrac{4 - .4}{4\%} - 4$ Steve Wilson, 9/06Raytown, MO 87 (3.2) $\dfrac{.\overline{4} - 4\%}{.\overline{4}\%} - 4$ Steve Wilson, 10/08Raytown, MO 88 (2.0) $44 + 44$ Dave Jones, 9/06Coventry, England 89 (2.4) $\dfrac{4 - .44}{4\%}$ Dave Jones, 11/06Coventry, England 90 (2.4) $\dfrac{4}{4\%} - \dfrac{4}{.4}$ Steve Wilson, 6/06Raytown, MO 91 (2.6) $\dfrac{4}{4\%} - \dfrac{4}{.\overline{4}}$ Steve Wilson, 1/06Raytown, MO 92 (2.2) $\dfrac{4}{4\%} - 4 - 4$ Carolyn Neptune, 6/06Prairie Village, KS 93 (3.4) $\dfrac{.4 - .\overline{4}\%}{.\overline{4}\%} + 4$ Steve Wilson, 10/08Raytown, MO 94 (2.4) $\dfrac{4 - .4}{4\%} + 4$ Steve Wilson, 9/06Raytown, MO 95 (2.4) $\dfrac{44}{.\overline{4}} - 4$ Dave Jones, 11/06Coventry, England 96 (2.4) $\dfrac{4 - 4 \times 4\%}{4\%}$ Dave Jones, 2/07Coventry, England 97 (2.4) $\dfrac{4 + 4\%}{4\%} - 4$ Dave Jones, 2/07Coventry, England 98 (2.4) $\dfrac{4 - (4 + 4)\%}{4\%}$ Dave Jones, 2/07Coventry, England 99 (2.2) $\dfrac{4}{4\%} - \dfrac44$ Carolyn Neptune, 4/06Prairie Village, KS 100 (2.2) $\dfrac{4}{4\%} + 4 - 4$ Steve Wilson, 1/06Raytown, MO 101 (2.2) $\dfrac{4}{4\%} + \dfrac44$ Anders Skjäl, 2/04Turku, Finland 102 (2.4) $\dfrac{4 + (4+4)\%}{4\%}$ Dave Jones, 2/07Coventry, England 103 (2.4) $\dfrac{44}{.\overline{4}} + 4$ Steve Wilson, 7/03Raytown, MO 104 (2.4) $\dfrac{4 + 4 \times 4\%}{4\%}$ Dave Jones, 4/07Coventry, England 105 (2.4) $\dfrac{4 + 4\%}{4\%} + 4$ Dave Jones, 4/07Coventry, England 106 (2.2) $\dfrac{44}{.4} - 4$ Dave Jones, 3/06Coventry, England 107 (3.6) $\dfrac{4 + (4! + 4)\%}{4\%}$ Steve Wilson, 12/07Raytown, MO 108 (2.2) $\dfrac{4}{4\%} + 4 + 4$ Carolyn Neptune, 4/06Prairie Village, KS 109 (2.4) $\dfrac{44 - .4}{.4}$ Steve Wilson, 4/03Raytown, MO 110 (2.4) $\dfrac{4}{4\%} + \dfrac{4}{.4}$ Carolyn Neptune, 6/06Prairie Village, KS 111 (2.0) $\dfrac{444}{4}$ Tim Murphy, 2/03Olathe, KS 112 (3.2) $4! \times 4 + 4 \times 4$ Adam Petrowsky, 5/03Lenexa, KS 113 (3.2) $\dfrac{.\overline{4} + 4\%}{.\overline{4}\%} + 4$ Paolo Pellegrini, 8/08Martina Franca, Italy 114 (2.2) $\dfrac{44}{.4} + 4$ John Kite, 4/03Lenexa, KS 115 (3.2) $\dfrac{.4 + \dfrac{.\overline{4}}{4}}{.\overline{4}\%}$ Steve Wilson, 10/08Raytown, MO 116 (2.2) $\dfrac{4}{4\%} + 4 \times 4$ Carolyn Neptune, 4/06Prairie Village, KS 117 (3.8) $\dfrac{4! + 4! + 4}{.\overline{4}}$ Paolo Pellegrini, 7/08Martina Franca, Italy 118 (3.2) $\dfrac{.\overline{4} + (4 + 4)\%}{.\overline{4}\%}$ Steve Wilson, 10/08Raytown, MO 119 (3.6) $\left( \dfrac{\sqrt{4}}{.4} \right)! - \dfrac44$ Steve Wilson, 9/03Raytown, MO 120 (2.2) $\dfrac{44 + 4}{.4}$ Dave Jones, 11/06Coventry, England 121 (3.2) $\sqrt{ \left( \dfrac{44}{4} \right)^4}$ Paolo Pellegrini, 7/08Martina Franca, Italy 122 (3.4) $\left(4 + \dfrac44 \right)! + \sqrt{4}$ Steve Wilson, 11/03Raytown, MO 123 (3.6) $\dfrac{44}{.\overline{4}} + 4!$ Anders Skjäl, 5/04Turku, Finland 124 (3.2) $\dfrac{4^4}{\sqrt{4}} - 4$ Steve Wilson, 1/05Raytown, MO 125 (2.2) $\dfrac{4 + \dfrac44}{4\%}$ Dave Jones, 11/06Coventry, England 126 (3.0) $\dfrac{.4 + 4 \times 4\%}{.\overline{4}\%}$ Paolo Pellegrini, 7/08Martina Franca, Italy 127 (3.4) $\dfrac{4^4 - \sqrt{4}}{\sqrt{4}}$ Anders Skjäl, 2/04Turku, Finland 128 (1.0) $4 \times 4 \times (4 + 4)$ Fredrik Jansson, 12/03Turku, Finland 129 (3.4) $\dfrac{4^4 + \sqrt{4}}{\sqrt{4}}$ Steve Wilson, 2/04Raytown, MO 130 (3.2) $\dfrac{4^4 + 4}{\sqrt{4}}$ Paolo Pellegrini, 7/08Martina Franca, Italy 131 (3.8) $\dfrac{4!}{.4 \times .\overline{4}} - 4$ Ralph Jeffords, 2/07Centreville, VA 132 (3.2) $\dfrac{4^4}{\sqrt{4}} + 4$ Carolyn Neptune, 2/04Prairie Village, KS 133 (4.0) $\dfrac{4!}{.4 \times .\overline{4}} - \sqrt{4}$ Steve Wilson, 3/06Raytown, MO 134 (2.8) $\dfrac{.4}{.\overline{4}\%} + 44$ Steve Wilson, 1/07Raytown, MO 135 (2.8) $\dfrac{\dfrac44 - .4}{.\overline{4}\%}$ Dave Jones, 4/07Coventry, England 136 (3.2) $\dfrac{.\overline{4} + 4 \times 4\%}{.\overline{4}\%}$ Steve Wilson, 10/08Raytown, MO 137 (4.0) $\dfrac{4!}{.4 \times .\overline{4}} + \sqrt{4}$ Steve Wilson, 3/06Raytown, MO 138 (3.6) $\dfrac{4! \times 4! - 4!}{4}$ Steve Wilson, 1/07Raytown, MO 139 (3.8) $\dfrac{4!}{.4 \times .\overline{4}} + 4$ Ralph Jeffords, 3/07Centreville, VA 140 (2.4) $\dfrac{4 + 4 \times .4}{4\%}$ Dave Jones, 4/07Coventry, England 141 (3.8) $\dfrac{4 - 4\%}{4! \pmf} - 4!$ Paolo Pellegrini, 8/08Martina Franca, Italy 142 (3.6) $4! \times (4 + \sqrt{4}) - \sqrt{4}$ Steve Wilson, 8/04Raytown, MO 143 (3.4) $\dfrac{4! \times 4! - 4}{4}$ Steve Wilson, 9/04Raytown, MO 144 (2.2) $\dfrac{4}{4\%} + 44$ Dave Jones, 10/06Coventry, England 145 (3.4) $\dfrac{4! \times 4! + 4}{4}$ Steve Wilson, 10/04Raytown, MO 146 (3.4) $\dfrac{4 + \sqrt{4}}{4\%} - 4$ Steve Wilson, 10/08Raytown, MO 147 (4.0) $\dfrac{4! \times 4 + \sqrt{4}}{\sqrt{.\overline{4}}}$ Carolyn Neptune, 11/04Prairie Village, KS 148 (3.4) $4! \times (4 + \sqrt{4}) + 4$ Steve Wilson, 2/07Raytown, MO 149 (3.4) $\dfrac{ \dfrac{4!}{4\%} - 4}{4}$ Steve Wilson, 10/08Raytown, MO 150 (2.4) $\dfrac{ \dfrac{4}{.4} - 4}{4\%}$ Dave Jones, 5/07Coventry, England 151 (3.4) $\dfrac{\dfrac{4!}{4\%} + 4}{4}$ Steve Wilson, 10/08Raytown, MO 152 (3.2) $44 \times 4 - 4!$ Carolyn Neptune, 11/06Prairie Village, KS 153 (3.6) $\dfrac{44 + 4!}{.\overline{4}}$ Ralph Jeffords, 5/07Centreville, VA 154 (3.4) $\dfrac{4 + \sqrt{4}}{4\%} + 4$ Steve Wilson, 2/05Raytown, MO 155 (3.8) $\dfrac{4 + \sqrt{4} + \sqrt{4\%}}{4\%}$ Steve Wilson, 3/05Raytown, MO 156 (3.2) $4^4 - \dfrac{4}{4\%}$ Carolyn Neptune, 3/07Prairie Village, KS 157 (4.2) $\sqrt[-\sqrt{.\overline{4}}]{4\%} + \sqrt[.4]{4}$ Paolo Pellegrini, 8/09Martina Franca, Italy 158 (3.6) $(4! - 4)^4 \pmf - \sqrt{4}$ Paolo Pellegrini, 8/08Martina Franca, Italy 159 (4.0) $\dfrac{4!}{.4 \times .\overline{4}} + 4!$ Ralph Jeffords, 3/07Centreville, VA 160 (2.0) $(44 - 4) \times 4$ Dave Jones, 12/06Coventry, England 161 (3.6) $\dfrac{4 - 4\%}{4! \pmf} - 4$ Paolo Pellegrini, 8/08Martina Franca, Italy 162 (3.6) $(4! - 4)^4 \pmf + \sqrt{4}$ Steve Wilson, 8/08Raytown, MO 163 (3.8) $\dfrac{4 - 4\%}{4! \pmf} - \sqrt{4}$ Paolo Pellegrini, 8/08Martina Franca, Italy 164 (3.4) $\dfrac{4^4 \% + 4}{4\%}$ Steve Wilson, 10/08Raytown, MO 165 (3.8) $\dfrac{44}{.4 \times \sqrt{.\overline{4}}}$ Steve Wilson, 11/05Raytown, MO 166 (3.8) $4^4 - \dfrac{.4}{.\overline{4}\%}$ Steve Wilson, 3/07Raytown, MO 167 (3.6) $\dfrac{4 + (4 + 4) \pmf}{4! \pmf}$ Steve Wilson, 6/08Raytown, MO 168 (3.2) $4 \times (44 - \sqrt{4})$ Carolyn Neptune, 3/07Prairie Village, KS 169 (3.6) $\sqrt{ \left(4 + \dfrac{4}{.\overline{4}} \right)^4}$ Steve Wilson, 4/06Raytown, MO 170 (3.4) $\dfrac{44 + 4!}{.4}$ Ralph Jeffords, 3/07Centreville, VA 171 (3.2) $\dfrac{.4 + .4 - 4\%}{.\overline{4}\%}$ Paolo Pellegrini, 5/08Martina Franca, Italy 172 (2.0) $44 \times 4 - 4$ Kimberly Grosdidier, 12/05Overland Park, KS 173 (4.0) $\dfrac{4 + \sqrt{4\%}}{4! \pmf} - \sqrt{4}$ Paolo Pellegrini, 8/08Martina Franca, Italy 174 (3.2) $4 \times 44 - \sqrt{4}$ Carolyn Neptune, 1/06Prairie Village, KS 175 (3.4) $\dfrac{4! + 4}{4 \times 4\%}$ Steve Wilson, 10/08Raytown, MO 176 (3.0) $\dfrac{.4 + .4}{.\overline{4}\%} - 4$ Steve Wilson, 10/08Raytown, MO 177 (4.0) $\dfrac{4 + \sqrt{4\%}}{4! \pmf} + \sqrt{4}$ Paolo Pellegrini, 8/08Martina Franca, Italy 178 (3.2) $4 \times 44 + \sqrt{4}$ Carolyn Neptune, 1/06Prairie Village, KS 179 (3.4) $\dfrac{(4 + \sqrt{4})! - 4}{4}$ Steve Wilson, 4/07Raytown, MO 180 (2.0) $4 \times 44 + 4$ Nancy Vaughn, 3/03Shawnee, KS 181 (3.4) $\dfrac{(4 + \sqrt{4})! + 4}{4}$ Steve Wilson, 4/07Raytown, MO 182 (3.6) $\dfrac{(4 + \sqrt{4})!}{4} + \sqrt{4}$ Steve Wilson, 4/07Raytown, MO 183 (4.4) $\dfrac{ \dfrac{4!}{\sqrt{4\%}} + \sqrt{4}}{\sqrt{.\overline{4}}}$ Steve Wilson, 5/07Raytown, MO 184 (3.0) $\dfrac{.4 + .4}{.\overline{4}\%} + 4$ Steve Wilson, 10/08Raytown, MO 185 (3.4) $\dfrac{4.44}{4! \pmf}$ Paolo Pellegrini, 7/08Martina Franca, Italy 186 (3.2) $\dfrac{.4 + .\overline{4}}{.\overline{4}\%} - 4$ Steve Wilson, 7/08Raytown, MO 187 (4.0) $\dfrac{4 - (4! + \sqrt{4})\%}{(\sqrt{4})\%}$ Steve Wilson, 1/08Raytown, MO 188 (3.2) $4! \times (4 + 4) - 4$ Anders Skjäl, 12/03Turku, Finland 189 (3.0) $\dfrac{44\% + .4}{.\overline{4}\%}$ Paolo Pellegrini, 5/08Martina Franca, Italy 190 (2.4) $\dfrac{4 + 4 - .4}{4\%}$ Dave Jones, 5/07Coventry, England 191 (3.8) $\dfrac{4}{(\sqrt{4})\%} - \dfrac{4}{.\overline{4}}$ Steve Wilson, 5/07Raytown, MO 192 (2.0) $4 \times (44 + 4)$ Carolyn Neptune, 3/06Prairie Village, KS 193 (4.4) $\sqrt{\sqrt{ .\overline{4}\% ^{-4}}} - \sqrt[.4]{4}$ Steve Wilson, 12/08Raytown, MO 194 (3.2) $\dfrac{.4 + .\overline{4}}{.\overline{4}\%} + 4$ Paolo Pellegrini, 7/08Martina Franca, Italy 195 (3.6) $\dfrac{4 + 4 - \sqrt{4\%}}{4\%}$ Paolo Pellegrini, 7/08Martina Franca, Italy 196 (2.2) $\dfrac{4 + 4}{4\%} - 4$ Dave Jones, 3/06Coventry, England 197 (3.8) $\dfrac{4 - \dfrac{4!\%}{4}}{(\sqrt{4})\%}$ Steve Wilson, 12/07Raytown, MO 198 (3.4) $\dfrac{4 + 4}{4\%} - \sqrt{4}$ Carolyn Neptune, 11/06Prairie Village, KS 199 (2.4) $\dfrac{4 + 4 - 4\%}{4\%}$ Dave Jones, 5/07Coventry, England 200 (2.2) $\dfrac{4}{(4 + 4)\%} \times 4$ Paolo Pellegrini, 7/08Martina Franca, Italy 201 (2.4) $\dfrac{4 + 4 + 4\%}{4\%}$ Dave Jones, 5/07Coventry, England 202 (3.4) $\dfrac{4 + 4}{4\%} + \sqrt{4}$ Carolyn Neptune, 11/06Prairie Village, KS 203 (3.8) $\dfrac{4 + \dfrac{4!\%}{4}}{(\sqrt{4})\%}$ Steve Wilson, 12/07Raytown, MO 204 (2.2) $\dfrac{4 + 4}{4\%} + 4$ Dave Jones, 3/06Coventry, England 205 (3.8) $\dfrac{4}{(\sqrt{4})\%} + \dfrac{\sqrt{4}}{.4}$ Steve Wilson, 7/07Raytown, MO 206 (3.4) $4^4 - \dfrac{\sqrt{4}}{4\%}$ Steve Wilson, 10/08Raytown, MO 207 (3.6) $\dfrac{4! \times 4 - 4}{.\overline{4}}$ Paolo Pellegrini, 5/08Martina Franca, Italy 208 (3.4) $4^4 - 4! - 4!$ Steve Wilson, 6/05Raytown, MO 209 (3.8) $\dfrac{4}{(\sqrt{4})\%} + \dfrac{4}{.\overline{4}}$ Steve Wilson, 7/07Raytown, MO 210 (2.2) $\dfrac{4.4 + 4}{4\%}$ Dave Jones, 12/06Coventry, England 211 (4.0) $\dfrac{4 + (4! - \sqrt{4})\%}{(\sqrt{4})\%}$ Steve Wilson, 1/08Raytown, MO 212 (3.0) $4^4 - 44$ Ralph Jeffords, 5/07Centreville, VA 213 (4.0) $\dfrac{4 + (4! + \sqrt{4})\%}{(\sqrt{4})\%}$ Steve Wilson, 4/08Raytown, MO 214 (3.8) $\dfrac{4}{.\overline{4}} \times 4! - \sqrt{4}$ Steve Wilson, 8/07Raytown, MO 215 (2.8) $\dfrac{ \dfrac{4}{.\overline{4}} - .4}{4\%}$ Dave Jones, 5/07Coventry, England 216 (2.6) $\dfrac{\dfrac{4}{4\%} - 4}{.\overline{4}}$ Dave Jones, 6/07Coventry, England 217 (4.0) $\dfrac{4! \times 4 + .\overline{4}}{.\overline{4}}$ Steve Wilson, 10/07Raytown, MO 218 (3.8) $\dfrac{4}{.\overline{4}} \times 4! + \sqrt{4}$ Steve Wilson, 9/05Raytown, MO 219 (3.8) $\sqrt[.4]{\dfrac{4}{.\overline{4}}} - 4!$ Steve Wilson, 8/07Raytown, MO 220 (3.4) $\sqrt{4} \times \dfrac{44}{.4}$ Ralph Jeffords, 4/07Centreville, VA 221 (2.6) $\dfrac{4}{4\% \times .\overline{4}} - 4$ Ralph Jeffords, 1/07Centreville, VA 222 (3.2) $\dfrac{444}{\sqrt{4}}$ Carolyn Neptune, 1/06Prairie Village, KS 223 (3.8) $\dfrac{4}{4\% \times .\overline{4}} - \sqrt{4}$ Ralph Jeffords, 1/07Centreville, VA 224 (2.6) $\dfrac{ \dfrac{4}{.\overline{4}\%} - 4}{4}$ Dave Jones, 6/07Coventry, England 225 (2.6) $\dfrac{4}{4\% \times .\overline{44}}$ Ralph Jeffords, 1/07Centreville, VA 226 (2.6) $\dfrac{ \dfrac{4}{.\overline{4}\%} + 4}{4}$ Dave Jones, 6/07Coventry, England 227 (3.8) $\dfrac{4}{4\% \times .\overline{4}} + \sqrt{4}$ Steve Wilson, 8/07Raytown, MO 228 (3.2) $4^4 - 4! - 4$ Steve Wilson, 7/05Raytown, MO 229 (2.6) $\dfrac{4}{4\% \times .\overline{4}} + 4$ Ralph Jeffords, 1/07Centreville, VA 230 (3.4) $4^4 - 4! - \sqrt{4}$ Ralph Jeffords, 5/07Centreville, VA 231 (3.8) $\dfrac{ \dfrac{4}{.\overline{4}\%} + 4!}{4}$ Steve Wilson, 1/08Raytown, MO 232 (3.4) $\sqrt{(4 \times 4)^4} - 4!$ Steve Wilson, 2/08Raytown, MO 233 (4.2) $\sqrt{ \sqrt{ .\overline{4}\% ^{-4}}} + 4 + 4$ Steve Wilson, 12/08Raytown, MO 234 (2.6) $\dfrac{ \dfrac{4}{4\%} + 4}{.\overline{4}}$ Dave Jones, 6/07Coventry, England 235 (2.8) $\dfrac{ \dfrac{4}{.\overline{4}} + .4}{4\%}$ Dave Jones, 6/07Coventry, England 236 (3.2) $4^4 - 4! + 4$ Ralph Jeffords, 7/07Centreville, VA 237 (4.2) $\dfrac{ \dfrac{\sqrt{4}}{.\overline{4}\%} + 4!}{\sqrt{4}}$ Paolo Pellegrini, 8/08Martina Franca, Italy 238 (3.6) $\dfrac{4}{.4} \times 4! - \sqrt{4}$ Steve Wilson, 9/05Raytown, MO 239 (3.6) $\sqrt[.4]{\dfrac{4}{.\overline{4}}} - 4$ Steve Wilson, 8/07Raytown, MO 240 (2.4) $\dfrac{ \dfrac{4}{4\%} - 4}{.4}$ Dave Jones, 7/07Coventry, England 241 (3.2) $\dfrac{ \dfrac{.\overline{4}}{.4\%} - 4}{.\overline{4}}$ Paolo Pellegrini, 8/08Martina Franca, Italy 242 (3.6) $4! \times \dfrac{4}{.4} + \sqrt{4}$ Steve Wilson, 2/08Raytown, MO 243 (3.4) $\sqrt[ \sqrt{4\%}]{4 - \dfrac44}$ Steve Wilson, 10/08Raytown, MO 244 (3.4) $4^4 - \dfrac{4!}{\sqrt{4}}$ Ralph Jeffords, 7/07Centreville, VA 245 (3.6) $\dfrac{4! \times 4 + \sqrt{4}}{.4}$ Steve Wilson, 5/08Raytown, MO 246 (2.4) $\dfrac{4}{4 \times .4\%} - 4$ Dave Jones, 7/07Coventry, England 247 (3.4) $4^4 - \dfrac{4}{.\overline{4}}$ Ralph Jeffords, 7/07Centreville, VA 248 (3.0) $4^4 - 4 - 4$ Kelsey Thomas, 2/05Olathe, KS 249 (2.4) $\dfrac{ \dfrac{4}{.4\%} - 4}{4}$ Dave Jones, 8/07Coventry, England 250 (2.8) $\dfrac{4.\overline{4}}{4 \times .\overline{4}\%}$ Dave Jones, 1/08Coventry, England 251 (2.4) $\dfrac{ \dfrac{4}{.4\%} + 4}{4}$ Dave Jones, 8/07Coventry, England 252 (3.2) $4^4 - \sqrt{4 \times 4}$ Ralph Jeffords, 9/07Centreville, VA 253 (3.6) $4^4 - \sqrt{ \dfrac{4}{.\overline{4}}}$ Ralph Jeffords, 7/07Centreville, VA 254 (2.4) $\dfrac{4}{4 \times .4\%} + 4$ Dave Jones, 8/07Coventry, England 255 (3.0) $4^4 - \dfrac44$ Jared Northrup, 4/03Lawrence, KS 256 (1.0) $4 \times 4 \times 4 \times 4$ Joseph Mavungu, 3/03Olathe, KS 257 (3.0) $4^4 + \dfrac44$ Cate Henderson, 4/05Merriam, KS 258 (3.2) $4^4 + 4 - \sqrt{4}$ Steve Wilson, 10/05Raytown, MO 259 (3.2) $\dfrac{ \dfrac{.\overline{4}}{.4\%} + 4}{.\overline{4}}$ Steve Wilson, 10/08Raytown, MO 260 (2.4) $\dfrac{ \dfrac{4}{4\%} + 4}{.4}$ Dave Jones, 8/07Coventry, England 261 (3.4) $4^4 + \dfrac{\sqrt{4}}{.4}$ Carolyn Neptune, 5/07Prairie Village, KS 262 (3.2) $4^4 + 4 + \sqrt{4}$ Steve Wilson, 11/07Raytown, MO 263 (4.8) $4^4 + 4 + \coth \ln \sqrt{\sqrt{4}}$ Steve Wilson, 1/08Raytown, MO 264 (3.0) $4^4 + 4 + 4$ Sydney Barker, 5/03Stilwell, KS 265 (3.4) $4^4 + \dfrac{4}{.\overline{4}}$ Steve Wilson, 11/07Raytown, MO 266 (3.2) $4^4 + \dfrac{4}{.4}$ Carolyn Neptune, 3/07Prairie Village, KS 267 (3.8) $\sqrt[.4]{\dfrac{4}{.\overline{4}}} + 4!$ Steve Wilson, 8/07Raytown, MO 268 (3.4) $4^4 + \dfrac{4!}{\sqrt{4}}$ Steve Wilson, 11/05Raytown, MO 269 (4.2) $\sqrt{\sqrt{ .\overline{4}\% ^{-4}}} + 44$ Steve Wilson, 12/08Raytown, MO 270 (3.0) $\dfrac{4 \times .4 - .4}{.\overline{4}\%}$ Steve Wilson, 10/08Raytown, MO 271 (4.4) $4^4 + \sqrt{\sqrt{\sqrt{ .\overline{4}\% ^{-4}}}}$ Steve Wilson, 12/08Raytown, MO 272 (3.0) $4^4 + 4 \times 4$ Cate Henderson, 5/05Merriam, KS 273 (4.6) $\sqrt{\sqrt{ .\overline{4}\% ^{-4}}} + 4! + 4!$ Steve Wilson, 12/08Raytown, MO 274 (3.4) $\dfrac{4}{4 \times 4 \pmf} + 4!$ Steve Wilson, 10/08Raytown, MO 275 (2.2) $\dfrac{44}{4 \times 4\%}$ Dave Jones, 3/06Coventry, England 276 (3.2) $4^4 + 4! - 4$ Steve Wilson, 11/07Raytown, MO 277 (4.6) $4^4 + \cot\arctan(4\%) - 4$ Steve Wilson, 9/23Lawrence, KS 278 (3.4) $4^4 + 4! - \sqrt{4}$ Steve Wilson, 11/05Raytown, MO 279 (3.8) $\dfrac{\dfrac{4}{4\%} + 4!}{.\overline{4}}$ Paolo Pellegrini, 5/08Martina Franca, Italy 280 (3.4) $\sqrt{(4 \times 4)^4} + 4!$ Steve Wilson, 2/08Raytown, MO 281 (3.8) $4^4 + \sqrt{\sqrt{ 4\% ^{-4}}}$ Paolo Pellegrini, 8/09Martina Franca, Italy 282 (3.4) $4^4 + 4! + \sqrt{4}$ Steve Wilson, 5/08Raytown, MO 283 (4.8) $4^4 + \cot\arctan(4\%) + \sqrt{4}$ Steve Wilson, 9/23Lawrence, KS 284 (3.2) $4^4 + 4! + 4$ Steve Wilson, 11/07Raytown, MO 285 (4.2) $\dfrac{ 4! + \dfrac{.4}{.\overline{4}\%}}{.4}$ Paolo Pellegrini, 6/08Martina Franca, Italy 286 (3.8) $4^4 + \sqrt{ \dfrac{4}{.\overline{4}\%}}$ Ralph Jeffords, 9/07Centreville, VA 287 (3.8) $\dfrac{4! \times 4! - \sqrt{4}}{\sqrt{4}}$ Steve Wilson, 5/08Raytown, MO 288 (3.2) $4^4 + \sqrt[.4]{4}$ Ralph Jeffords, 12/07Centreville, VA 289 (3.8) $\dfrac{4! \times 4! + \sqrt{4}}{\sqrt{4}}$ Steve Wilson, 5/08Raytown, MO 290 (3.8) $4! \times \dfrac{4!}{\sqrt{4}} + \sqrt{4}$ Steve Wilson, 4/08Raytown, MO 291 (4.4) $\sqrt{ \dfrac{4}{.\overline{4}\%\%}} - \dfrac{4}{.\overline{4}}$ Ralph Jeffords, 10/07Centreville, VA 292 (3.6) $4! \times \dfrac{4!}{\sqrt{4}} + 4$ Steve Wilson, 4/08Raytown, MO 293 (4.8) $\coth\ln\coth\arsinh(4 + 4 + 4) + 4$ Steve Wilson, 9/23Lawrence, KS 294 (4.0) $\dfrac{4! - 4.4}{\sqrt{.\overline{4}\%}}$ Steve Wilson, 11/08Raytown, MO 295 (3.6) $\dfrac{4! - .4}{(4 + 4)\%}$ Paolo Pellegrini, 5/08Martina Franca, Italy 296 (3.4) $\dfrac{4!}{(4 + 4)\%} - 4$ Steve Wilson, 10/08Raytown, MO 297 (3.8) $\dfrac{4! - 4!\%}{(4 + 4)\%}$ Steve Wilson, 7/24Lawrence, KS 298 (3.6) $\dfrac{ \dfrac{4!}{4\%} - 4}{\sqrt{4}}$ Steve Wilson, 5/08Raytown, MO 299 (3.8) $\dfrac{ \dfrac{4!}{4\%} - \sqrt{4}}{\sqrt{4}}$ Steve Wilson, 5/08Raytown, MO 300 (2.2) $\dfrac{4 + 4 + 4}{4\%}$ Dave Jones, 3/06Coventry, England 301 (3.8) $\dfrac{ \dfrac{4!}{4\%} + \sqrt{4}}{\sqrt{4}}$ Steve Wilson, 5/08Raytown, MO 302 (3.6) $\dfrac{ \dfrac{4!}{4\%} + 4}{\sqrt{4}}$ Steve Wilson, 5/08Raytown, MO 303 (3.8) $\dfrac{4! + 4!\%}{(4 + 4)\%}$ Steve Wilson, 7/24Lawrence, KS 304 (3.4) $\dfrac{4!}{(4 + 4)\%} + 4$ Paolo Pellegrini, 5/08Martina Franca, Italy 305 (3.6) $\dfrac{4! + .4}{(4 + 4)\%}$ Paolo Pellegrini, 5/08Martina Franca, Italy 306 (3.4) $4^4 + \dfrac{\sqrt{4}}{4\%}$ Paolo Pellegrini, 5/08Martina Franca, Italy 307 (4.6) $4^4 + 4! \times \cosh\ln 4$ Steve Wilson, 9/23Lawrence, KS 308 (4.0) $\sqrt{\dfrac{4}{.\overline{4}\%\%}} + 4 + 4$ Ralph Jeffords, 2/08Centreville, VA 309 (4.4) $\sqrt{\dfrac{4}{.\overline{4}\%\%}} + \dfrac{4}{.\overline{4}}$ Steve Wilson, 5/08Raytown, MO 310 (3.2) $\dfrac{4 \times .\overline{4} - .4}{.\overline{4}\%}$ Steve Wilson, 10/08Raytown, MO 311 (5.2) $\cot\arctan (4\pm) + \dfrac{4! + .4}{.4}$ Steve Wilson, 9/08Raytown, MO 312 (3.6) $4! \times \left(4 + \dfrac{4}{.\overline{4}} \right)$ Paolo Pellegrini, 5/08Martina Franca, Italy 313 (4.8) $\dfrac{\cot\arctan(4\%\%) + 4}{4 + 4}$ Steve Wilson, 9/23Lawrence, KS 314 (4.6) $\cot\arctan (4\pm) + 4 \times 4 \times 4$ Steve Wilson, 6/08Raytown, MO 315 (2.8) $\dfrac{\dfrac44 + .4}{.\overline{4}\%}$ Dave Jones, 11/07Coventry, England 316 (3.4) $4^4 + \dfrac{4!}{.4}$ Paolo Pellegrini, 5/08Martina Franca, Italy 317 (5.2) $\cot\arctan (.\overline{4}\%) + 4 \times 4! - 4$ Steve Wilson, 7/08Raytown, MO 318 (3.8) $\sqrt{ \dfrac{4}{4^{-4}\%}} - \sqrt{4}$ Paolo Pellegrini, 8/09Martina Franca, Italy 319 (4.8) $\dfrac{4}{\left(\cosh\ln\sqrt{4}\right)\%} - \dfrac44$ Steve Wilson, 9/23Lawrence, KS 320 (3.2) $(4! - 4) \times 4 \times 4$ Paolo Pellegrini, 6/08Martina Franca, Italy 321 (4.4) $\sqrt{\sqrt{ .\overline{4}\% ^{-4}}} + 4! \times 4$ Steve Wilson, 12/08Raytown, MO 322 (3.8) $\sqrt{ \dfrac{4}{4^{-4}\%}} + \sqrt{4}$ Steve Wilson, 8/09Raytown, MO 323 (5.4) $\cot\arctan (.\overline{4}\%) + \dfrac{4}{4\%} - \sqrt{4}$ Steve Wilson, 7/08Raytown, MO 324 (3.0) $\dfrac{4}{.\overline{4}\%} \times (.4 - 4\%)$ Paolo Pellegrini, 6/08Martina Franca, Italy 325 (2.6) $\dfrac{4 + \dfrac{4}{.\overline{4}}}{4\%}$ Dave Jones, 11/07Coventry, England 326 (4.2) $\dfrac{4! - \sqrt{4}}{\sqrt{.\overline{4}\%}} - 4$ Steve Wilson, 11/08Raytown, MO 327 (5.4) $\cot\arctan (.\overline{4}\%) + \dfrac{4}{4\%} + \sqrt{4}$ Steve Wilson, 7/08Raytown, MO 328 (3.6) $\dfrac{4 + 4^4\%}{(\sqrt{4})\%}$ Steve Wilson, 7/24Lawrence, KS 329 (5.0) $\dfrac{4! - \sqrt{4} - \sqrt{.\overline{4}\%}}{\sqrt{.\overline{4}\%}}$ Steve Wilson, 11/08Raytown, MO 330 (4.2) $\dfrac{4! - \sqrt{4}}{\sqrt{.\overline{44}\%}}$ Steve Wilson, 7/24Lawrence, KS 331 (5.0) $\dfrac{4! - \sqrt{4} + \sqrt{.\overline{4}\%}}{\sqrt{.\overline{4}\%}}$ Steve Wilson, 11/08Raytown, MO 332 (4.2) $\dfrac{4!}{\sqrt{.\overline{4}\%}} - 4! - 4$ Paolo Pellegrini, 6/08Martina Franca, Italy 333 (3.8) $\dfrac{\sqrt{4}}{4! \pmf} \times (4 - 4 \pm)$ Paolo Pellegrini, 8/08Martina Franca, Italy 334 (4.2) $\dfrac{4! - \sqrt{4}}{\sqrt{.\overline{4}\%}} + 4$ Steve Wilson, 11/08Raytown, MO 335 (4.8) $\dfrac{4!}{\sqrt{.\overline{4}\%}} - \sqrt{\sqrt{ 4\%^{-4}}}$ Steve Wilson, 10/08Raytown, MO 336 (3.4) $4! \times \left(4 + \dfrac{4}{.4} \right)$ Paolo Pellegrini, 5/08Martina Franca, Italy 337 (4.8) $4^4 + \left(\coth\ln\sqrt{\sqrt{4}}\right)^4$ Steve Wilson, 9/23Lawrence, KS 338 (3.8) $\dfrac{\sqrt{(4! + \sqrt{4})^4}}{\sqrt{4}}$ Steve Wilson, 5/08Raytown, MO 339 (4.6) $\dfrac{4! + \sqrt{4\%}}{\sqrt{.\overline{4}\%}} - 4!$ Steve Wilson, 11/08Raytown, MO 340 (3.4) $\dfrac{.4 + \dfrac{.\overline{4}}{.4}}{.\overline{4}\%}$ Paolo Pellegrini, 7/08Martina Franca, Italy 341 (4.8) $\coth\left(4 \times \arsinh\sqrt{\dfrac{4!}{4}}\right) + 4$ Steve Wilson, 9/23Lawrence, KS 342 (4.2) $\dfrac{(4 - \sqrt{4\%}) \times .4}{.\overline{4}\%}$ Paolo Pellegrini, 8/08Martina Franca, Italy 343 (4.0) $\sqrt{\sqrt{\sqrt{\left(\dfrac{4! + 4}{4}\right)^{4!}}}}$ Steve Wilson, 9/23Lawrence, KS 344 (2.8) $4 \times \left( \dfrac{.4}{.\overline{4}\%} - 4 \right)$ Dave Jones, 11/07Coventry, England 345 (4.0) $\dfrac{4! - \dfrac44}{\sqrt{.\overline{4}\%}}$ Paolo Pellegrini, 6/08Martina Franca, Italy 346 (3.8) $4^4 + \dfrac{.4}{.\overline{4}\%}$ Paolo Pellegrini, 6/08Martina Franca, Italy 347 (5.8) $\cot\arctan (.\overline{4}\%) + \left( \dfrac{\sqrt{4}}{.4} \right)! + \sqrt{4}$ Steve Wilson, 9/08Raytown, MO 348 (3.8) $\dfrac{4^4 - 4!}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 6/08Martina Franca, Italy 349 (5.4) $\cot\arctan (.\overline{4}\%) + \dfrac{4}{4\%} + 4!$ Steve Wilson, 7/08Raytown, MO 350 (2.4) $\dfrac{ \dfrac{4}{.4} + 4}{4\%}$ Dave Jones, 8/07Coventry, England 351 (3.0) $\dfrac{4 \times .4 - 4\%}{.\overline{4}\%}$ Paolo Pellegrini, 6/08Martina Franca, Italy 352 (2.0) $44 \times (4 + 4)$ Brad Anderson, 9/06Overland Park, KS 353 (4.4) $\dfrac{4! - \sqrt{4\%}}{\sqrt{.\overline{4}\%}} - 4$ Steve Wilson, 11/08Raytown, MO 354 (4.0) $\dfrac{\sqrt{4}}{.\overline{4}\%} - 4! \times 4$ Paolo Pellegrini, 6/08Martina Franca, Italy 355 (4.4) $\dfrac{4!}{\sqrt{.\overline{4}\%}} - \dfrac{\sqrt{4}}{.4}$ Steve Wilson, 7/08Raytown, MO 356 (2.8) $\dfrac{.4}{.\overline{4}\%} \times 4 - 4$ Dave Jones, 11/07Coventry, England 357 (4.4) $\dfrac{4! - \dfrac{.4}{\sqrt{4}}}{\sqrt{.\overline{4}\%}}$ Steve Wilson, 11/08Raytown, MO 358 (4.0) $\dfrac{.4}{.\overline{4}\%} \times 4 - \sqrt{4}$ Steve Wilson, 7/08Raytown, MO 359 (3.4) $\dfrac{4 \times .4 - .\overline{4}\%}{.\overline{4}\%}$ Paolo Pellegrini, 6/08Martina Franca, Italy 360 (2.4) $\dfrac{4 \times 4}{4.\overline{4}\%}$ Dave Jones, 12/06Coventry, England 361 (3.4) $\dfrac{4 \times .4 + .\overline{4}\%}{.\overline{4}\%}$ Paolo Pellegrini, 6/08Martina Franca, Italy 362 (4.0) $\dfrac{.4}{.\overline{4}\%} \times 4 + \sqrt{4}$ Steve Wilson, 7/08Raytown, MO 363 (4.4) $\dfrac{4! + \dfrac{.4}{\sqrt{4}}}{\sqrt{.\overline{4}\%}}$ Steve Wilson, 11/08Raytown, MO 364 (2.8) $\dfrac{.4}{.\overline{4}\%} \times 4 + 4$ Dave Jones, 11/07Coventry, England 365 (4.4) $\dfrac{4!}{\sqrt{.\overline{4}\%}} + \dfrac{\sqrt{4}}{.4}$ Steve Wilson, 7/08Raytown, MO 366 (4.2) $\dfrac{4!}{\sqrt{.\overline{4}\%}} + 4 + \sqrt{4}$ Steve Wilson, 7/08Raytown, MO 367 (4.4) $\dfrac{4! + \sqrt{4\%}}{\sqrt{.\overline{4}\%}} + 4$ Steve Wilson, 11/08Raytown, MO 368 (3.2) $(4 \times 4! - 4) \times 4$ Paolo Pellegrini, 6/08Martina Franca, Italy 369 (3.0) $\dfrac{4 \times .4 + 4\%}{.\overline{4}\%}$ Paolo Pellegrini, 6/08Martina Franca, Italy 370 (4.0) $\dfrac{4! + \dfrac{\sqrt{4}}{4\%}}{\sqrt{4\%}}$ Paolo Pellegrini, 6/08Martina Franca, Italy 371 (3.8) $\dfrac{4}{4! \times .\overline{4} \pmf} - 4$ Paolo Pellegrini, 8/08Martina Franca, Italy 372 (3.8) $\dfrac{ (4 + \sqrt{4})! + 4!}{\sqrt{4}}$ Steve Wilson, 9/08Raytown, MO 373 (4.0) $\dfrac{4}{4! \times .\overline{4} \pmf} - \sqrt{4}$ Paolo Pellegrini, 6/08Martina Franca, Italy 374 (4.0) $\dfrac{ \dfrac{4}{.\overline{4}\pmf} - 4!}{4!}$ Paolo Pellegrini, 8/08Martina Franca, Italy 375 (3.4) $\dfrac{.4}{\left( \dfrac{.\overline{4}}{4} - .\overline{4}\% \right)\%}$ Paolo Pellegrini, 6/08Martina Franca, Italy 376 (2.8) $4 \times \left( 4 + \dfrac{.4}{.\overline{4}\%} \right)$ Dave Jones, 1/08Coventry, England 377 (4.0) $\dfrac{4}{4! \times .\overline{4} \pmf} + \sqrt{4}$ Paolo Pellegrini, 8/08Martina Franca, Italy 378 (3.6) $\dfrac{4^4 - 4}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 6/08Martina Franca, Italy 379 (3.8) $\dfrac{4}{4! \times .\overline{4} \pmf} + 4$ Paolo Pellegrini, 8/08Martina Franca, Italy 380 (3.2) $4 \times 4! \times 4 - 4$ Steve Wilson, 6/08Raytown, MO 381 (3.8) $\dfrac{4^4 - \sqrt{4}}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 6/08Martina Franca, Italy 382 (3.4) $4 \times 4! \times 4 - \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 383 (4.2) $\dfrac{4^4 - \sqrt{.\overline{4}}}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 8/08Martina Franca, Italy 384 (2.2) $4 \times \left( \dfrac{4}{4\%} - 4 \right)$ Dave Jones, 12/06Coventry, England 385 (4.2) $\dfrac{4^4 + \sqrt{.\overline{4}}}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 8/08Martina Franca, Italy 386 (3.4) $4 \times 4! \times 4 + \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 387 (3.8) $\dfrac{4^4 + \sqrt{4}}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 6/08Martina Franca, Italy 388 (3.2) $4 \times 4! \times 4 + 4$ Joseph Mavungu, 4/03Olathe, KS 389 (4.8) $4 \times (4! \times 4 + \cosh\ln\sqrt{4})$ Steve Wilson, 9/23Lawrence, KS 390 (2.4) $\dfrac{4 \times 4 - .4}{4\%}$ Dave Jones, 9/07Coventry, England 391 (3.2) $\dfrac{4 \times .\overline{4} - 4\%}{.\overline{4}\%}$ Paolo Pellegrini, 6/08Martina Franca, Italy 392 (3.4) $4 \times \left( \dfrac{4}{4\%} - \sqrt{4} \right)$ Steve Wilson, 6/08Raytown, MO 393 (5.2) $\left( \dfrac{\sqrt{4}}{4 \pmf} + 4! \right) \times \sinh \ln \sqrt{4}$ Steve Wilson, 9/08Raytown, MO 394 (3.6) $\dfrac{4 \times 4 - 4!\%}{4\%}$ Steve Wilson, 6/08Raytown, MO 395 (3.6) $\dfrac{4 \times 4 - \sqrt{4\%}}{4\%}$ Paolo Pellegrini, 6/08Martina Franca, Italy 396 (2.2) $\dfrac{4}{4\%} \times 4 - 4$ David Caton, 10/04Shawnee, KS 397 (4.6) $\dfrac{\sqrt{4} - (4! - .\overline{4})\%}{.\overline{4}\%}$ Steve Wilson, 10/08Raytown, MO 398 (3.4) $\dfrac{4}{4\%} \times 4 - \sqrt{4}$ Steve Wilson, 2/08Raytown, MO 399 (2.4) $\dfrac{4 \times 4 - 4\%}{4\%}$ Dave Jones, 9/07Coventry, England 400 (3.0) $(4 - .4) \times \dfrac{.\overline{4}}{.4\%}$ Paolo Pellegrini, 6/08Martina Franca, Italy