$\def\pm{{ ‰}} \def\pmf{{ ‰ \phantom.}} \def\pmm{{ ‰ \! ‰}} \def\pmmf{{ ‰ \! ‰ \phantom\%}} \DeclareMathOperator{\antilog}{antilog} \DeclareMathOperator{\arcsec}{arcsec} \DeclareMathOperator{\arccsc}{arccsc} \DeclareMathOperator{\sech}{sech} \DeclareMathOperator{\csch}{csch} \DeclareMathOperator{\arsinh}{arsinh} \DeclareMathOperator{\arcosh}{arcosh} \DeclareMathOperator{\arcsch}{arcsch}$

## 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.

 1601 (4.0) $\dfrac{\sqrt[.4]{4} + (\sqrt{4})\%}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1602 (3.6) $(4! - 4)^4 \% + \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1603 (5.0) $\dfrac{4}{(\cot\arctan 4)\%} + \log\left(\dfrac{4}{4\pmf}\right)$ Steve Wilson, 6/24Lawrence, KS 1604 (3.4) $(4! - 4)^4 \% + 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1605 (4.4) $\dfrac{(4 + (\sqrt{4})\%)\% + 4!\pmf}{4\%\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1606 (4.6) $\dfrac{4! \times .\overline{4} + 4\%}{\left(\sqrt{.\overline{4}}\right)\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1607 (5.4) $\dfrac{4}{(\cot\arctan 4)\%} + \cosh(\sqrt{4} \times \arcosh\sqrt{4})$ Steve Wilson, 5/24Lawrence, KS 1608 (4.2) $\dfrac{4 + (\sqrt{4})\%}{\left(\sqrt{\sqrt{4^{-4}}}\right)\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1609 (5.0) $\dfrac{4}{(\cot\arctan 4)\%} + \dfrac{4}{.\overline{4}}$ Steve Wilson, 5/24Lawrence, KS 1610 (4.0) $\dfrac{\sqrt[.4]{4} + \sqrt{4\%}}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1611 (3.8) $\dfrac{(4 + \sqrt{4})! - 4}{.\overline{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1612 (3.8) $4 \times \left( (4 + 4)!\% - \sqrt{4\%} \right)$ Paolo Pellegrini, 10/09Martina Franca, Italy 1613 (3.8) $(4 + 4)! \times 4\% + \sqrt{4\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1614 (4.6) $\dfrac{\sqrt{.\overline{4}} + 4\%}{.\overline{4}\pmf} + 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1615 (5.4) $\coth\ln\coth\arcosh(4! + 4) + 4! \times \sqrt{4}$ Steve Wilson, 11/23Lawrence, KS 1616 (3.8) $\dfrac{(4 + \sqrt{4})!}{.\overline{4}} - 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1617 (5.4) $\coth\ln\coth\arcosh(4! + 4) + \dfrac{\sqrt{4}}{4\%}$ Steve Wilson, 11/23Lawrence, KS 1618 (4.0) $\dfrac{(4 + \sqrt{4})!}{.\overline{4}} -\sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1619 (4.2) $\dfrac{(4 + \sqrt{4})! - .\overline{4}}{.\overline{4}}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1620 (3.4) $\dfrac{4}{(.\overline{4} - .\overline{4} \times .\overline{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1621 (4.2) $\dfrac{(4+\sqrt{4})! + .\overline{4}}{.\overline{4}}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1622 (4.0) $\dfrac{(4+\sqrt{4})!}{.\overline{4}} + \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1623 (5.4) $\dfrac{4}{(\cot\arctan 4)\%} + \cot\arctan(4\%) - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1624 (3.6) $(4! - 4)^4 \% + 4!$ Steve Wilson, 11/09Raytown, MO 1625 (3.6) $\dfrac{4! + \sqrt{4}}{4 \times 4\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1626 (4.0) $\dfrac{4 - 4\%}{4!\%\%} - 4!$ Steve Wilson, 11/09Raytown, MO 1627 (5.6) $\dfrac{\left(\ln\sqrt{\sqrt{\exp 4!}}\right) + 4}{.\overline{4}} - \sqrt{4}$ Steve Wilson, 4/24Lawrence, KS 1628 (4.8) $\dfrac{4}{(\cot\arctan 4)\%} + 4! + 4$ Steve Wilson, 5/24Lawrence, KS 1629 (3.8) $\dfrac{(4 + \sqrt{4})! + 4}{.\overline{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1630 (4.4) $\dfrac{.\overline{4} + (4! + 4)\%}{.\overline{4}\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1631 (5.2) $\dfrac{4}{(\cot\arctan 4)\%} + \cosh(\sqrt{4} \times \arcosh 4)$ Steve Wilson, 5/24Lawrence, KS 1632 (3.4) $(44 + 4!) \times 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1633 (5.2) $\dfrac{4}{(\cot\arctan 4)\%} + \cosh(\sqrt{4} \times \arsinh 4)$ Steve Wilson, 5/24Lawrence, KS 1634 (5.2) $\dfrac{4}{(\cot\arctan 4)\%} + 4! + (\antilog 4)\pm$ Steve Wilson, 5/24Lawrence, KS 1635 (4.6) $\dfrac{ \sqrt{.\overline{4}} + (4 + \sqrt{4})\%}{.\overline{4}\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1636 (5.4) $\dfrac{4}{(\cot\arctan 4)\%} + \dfrac{4!}{\sqrt{.\overline{4}}}$ Steve Wilson, 5/24Lawrence, KS 1637 (5.4) $\dfrac{4}{(\cot\arctan 4)\%} + \coth\ln\coth\arsinh 4 + 4$ Steve Wilson, 5/24Lawrence, KS 1638 (4.0) $\dfrac{4 + 4\pmf}{\left( \sqrt{4} + .\overline{4} \right)\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1639 (5.6) $\dfrac{4!}{(\csch\ln\sqrt{4})\%} - \cosh(4 \times \arsinh\sqrt{4})$ Steve Wilson, 5/24Lawrence, KS 1640 (3.4) $\dfrac{4 + 4^4 \%}{4\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1641 (4.0) $\dfrac{4 - 4\pmf}{4!\%\%} - 4!$ Steve Wilson, 11/09Raytown, MO 1642 (4.4) $\dfrac{4}{4!\%\%} - \sqrt{.\overline{4}} - 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1643 (5.8) $\dfrac{(\antilog 4)\pmf}{\sech(4 \times \arsinh\sqrt{4})} + \coth\ln\coth\arsinh 4$ Steve Wilson, 5/24Lawrence, KS 1644 (4.0) $\dfrac{(4 + \sqrt{4})!}{.\overline{4}} + 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1645 (5.2) $\dfrac{4}{(\cot\arctan 4)\%} + \dfrac{4!}{\csch\ln 4}$ Steve Wilson, 5/24Lawrence, KS 1646 (3.8) $\dfrac{4 - 4\%}{4!\%\%} - 4$ Steve Wilson, 11/09Raytown, MO 1647 (5.6) $\dfrac{4}{(\cot\arctan 4)\%} + \cosh(\sqrt{4} \times \arcosh\sqrt{4!})$ Steve Wilson, 5/24Lawrence, KS 1648 (4.0) $\left( \sqrt{\sqrt{4^{4!}}} + 4! \right) \times .4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1649 (4.0) $\sqrt[\sqrt{4\%}]{4} + \sqrt{4\%^{-4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1650 (3.8) $\dfrac{44}{4\% \times \sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1651 (4.2) $\dfrac{4 - (4 - 4!\%)\%}{4!\%\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1652 (4.0) $\dfrac{4 - 4\%}{4!\%\%} + \sqrt{4}$ Steve Wilson, 11/09Raytown, MO 1653 (5.6) $\dfrac{\left(\ln\sqrt{\sqrt{\exp 4!}}\right) + 4}{.\overline{4}} + 4!$ Steve Wilson, 4/24Lawrence, KS 1654 (3.8) $\dfrac{4 - 4\%}{4!\%\%} + 4$ Steve Wilson, 11/09Raytown, MO 1655 (4.0) $\dfrac{4 - (4! + 4)\pmf}{4!\%\%}$ Steve Wilson, 11/09Raytown, MO 1656 (3.6) $\dfrac{(4+4)!}{4!} - 4!$ Steve Wilson, 11/09Raytown, MO 1657 (5.6) $\dfrac{4}{(\cot\arctan 4)\%} + \coth\ln\coth\arsinh 4 + 4!$ Steve Wilson, 5/24Lawrence, KS 1658 (5.4) $\dfrac{\coth\ln\coth\arsinh 4 + 4 \times 4\%}{(\sqrt{4})\%}$ Steve Wilson, 5/24Lawrence, KS 1659 (3.8) $\dfrac{(4^4 + 4!)\%}{\sqrt{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1660 (4.6) $\dfrac{\sqrt{.\overline{4}} + 44\%}{\left(\sqrt{.\overline{4}} \right)\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1661 (3.8) $\dfrac{4 - 4\pmf}{4!\%\%} - 4$ Steve Wilson, 11/09Raytown, MO 1662 (4.2) $\dfrac{4}{4!\%\%} - \sqrt{.\overline{4}} - 4$ Steve Wilson, 11/09Raytown, MO 1663 (4.0) $\dfrac{4 - 4\pmf}{4!\%\%} - \sqrt{4}$ Steve Wilson, 11/09Raytown, MO 1664 (4.4) $\left(\sqrt{(\sqrt{4})\%^{-4}} - 4 \right) \times \sqrt{.\overline{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1665 (3.8) $\dfrac{4 - 4\pmf}{(\sqrt{4} + .4)\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1666 (4.2) $\dfrac{4}{(\sqrt{4} + .4)\pmf} - \sqrt{.\overline{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1667 (4.0) $\dfrac{4 - 4\pmf}{4!\%\%} + \sqrt{4}$ Steve Wilson, 11/09Raytown, MO 1668 (4.2) $\dfrac{4 + (\sqrt[.4]{4})\%\%}{4!\%\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1669 (3.8) $\dfrac{4 - 4\pmf}{4!\%\%} + 4$ Steve Wilson, 11/09Raytown, MO 1670 (3.8) $\dfrac{4 + (4+4)\pmf}{4!\%\%}$ Steve Wilson, 11/09Raytown, MO 1671 (4.0) $\dfrac{4 + (\sqrt{4})\%}{4!\%\%} - 4$ Steve Wilson, 11/09Raytown, MO 1672 (4.8) $\dfrac{4! \times \left(.\overline{4} + (\sqrt{4})\% \right)}{\left( \sqrt{.\overline{4}} \right)\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1673 (4.2) $\dfrac{4 + (\sqrt{4})\%}{4!\%\%} - \sqrt{4}$ Steve Wilson, 11/09Raytown, MO 1674 (4.0) $\dfrac{(4 + \sqrt{4})! + 4!}{.\overline{4}}$ Steve Wilson, 10/09Raytown, MO 1675 (4.0) $\dfrac{4 + (\sqrt{4})\%}{(\sqrt{4} + .4)\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1676 (3.4) $\dfrac{(4+4)!}{4!} - 4$ Steve Wilson, 11/09Raytown, MO 1677 (4.2) $\dfrac{4 + (\sqrt{4})\%}{4!\%\%} + \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1678 (3.6) $\dfrac{(4+4)!}{4!} - \sqrt{4}$ Steve Wilson, 11/09Raytown, MO 1679 (3.6) $\dfrac{(4+4)! - 4!}{4!}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1680 (3.6) $\dfrac{(4+4)!}{(\sqrt{4 \times 4})!}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1681 (3.6) $\dfrac{(4+4)! + 4!}{4!}$ Steve Wilson, 11/09Raytown, MO 1682 (3.6) $\dfrac{(4+4)!}{4!} + \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1683 (5.8) $\dfrac{\coth\ln 4 - (\coth\ln 4)\%}{\left(\sqrt{.\overline{44}}\right)\pmf}$ Steve Wilson, 5/24Lawrence, KS 1684 (3.4) $\dfrac{(4+4)!}{4!} + 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1685 (3.8) $\dfrac{4 + 44\pmf}{4!\%\%}$ Steve Wilson, 10/09Raytown, MO 1686 (5.6) $\dfrac{(4+4)!}{4!} + \Gamma(4)$ Steve Wilson, 5/24Lawrence, KS 1687 (5.8) $\dfrac{\coth\ln 4 - (\coth\ln 4)\%}{\left(\sqrt{.\overline{4}}\right)\pmf} + 4$ Steve Wilson, 5/24Lawrence, KS 1688 (5.6) $\dfrac{\coth\ln 4}{\left(\sqrt{.\overline{4}}\right)\pmf} - \dfrac{4!}{\sqrt{4}}$ Steve Wilson, 5/24Lawrence, KS 1689 (4.0) $\dfrac{4 - 4\pmf}{4!\%\%} + 4!$ Steve Wilson, 11/09Raytown, MO 1690 (3.8) $\dfrac{\sqrt{(4! + \sqrt{4})^4}}{.4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1691 (5.6) $\dfrac{\coth\ln 4}{\left(\sqrt{.\overline{4}}\right)\pmf} - \dfrac{4}{.\overline{4}}$ Steve Wilson, 5/24Lawrence, KS 1692 (4.2) $(4 - 4!\pm) \times \dfrac{\sqrt{4}}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1693 (5.6) $\dfrac{\coth\ln 4 - (\sqrt{4})\pmf}{\left(\sqrt{.\overline{4}}\right)\pmf} - 4$ Steve Wilson, 5/24Lawrence, KS 1694 (5.2) $\dfrac{4 + 4!\%}{(\cot\arctan 4)\%} - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1695 (4.4) $\dfrac{4 + (\sqrt{4})\%\%}{(4!\% - 4\pm)\%\phantom8}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1696 (4.2) $\dfrac{4 + 4!\%}{\left(\sqrt{\sqrt{4^{-4}}}\right)\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1697 (5.6) $\dfrac{\coth\ln 4}{\left(\sqrt{.\overline{4}}\right)\pmf} - \log\left(\dfrac{4}{4\pmf}\right)$ Steve Wilson, 6/24Lawrence, KS 1698 (5.2) $\dfrac{4 + 4!\%}{(\cot\arctan 4)\%} + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1699 (4.2) $\dfrac{4 + (\sqrt{4})\%}{4!\%\%} + 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1700 (3.0) $\dfrac{4 + 4 - .\overline{4}}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1701 (4.4) $\dfrac{\sqrt{4} + 4!\%}{\left(\sqrt[.4]{.\overline{4}} \right)\%}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1702 (5.4) $\dfrac{\coth\ln 4}{\left(\sqrt{.\overline{4}}\right)\pmf} + \dfrac{4}{\sqrt{4}}$ Steve Wilson, 5/24Lawrence, KS 1703 (5.6) $\dfrac{\coth\ln 4}{\left(\sqrt{.\overline{4}}\right)\pmf} + \log\left(\dfrac{4}{4\pmf}\right)$ Steve Wilson, 6/24Lawrence, KS 1704 (3.6) $\dfrac{(4+4)!}{4!} + 4!$ Steve Wilson, 11/09Raytown, MO 1705 (4.2) $\dfrac{\left( \sqrt{\sqrt{4^{4!}}} - 4 \right)\%}{4!\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1706 (4.8) $\dfrac{\left(\sqrt{.\overline{4}}\right)\%}{4^{-4}\pm} - \sqrt{.\overline{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1707 (5.6) $\dfrac{\coth\ln 4 + (\sqrt{4})\pmf}{\left(\sqrt{.\overline{4}}\right)\pmf} + 4$ Steve Wilson, 5/24Lawrence, KS 1708 (5.2) $\dfrac{\coth\ln 4}{\left(\sqrt{.\overline{4}}\right)\pmf} + 4 + 4$ Steve Wilson, 5/24Lawrence, KS 1709 (5.6) $\dfrac{\coth\ln 4}{\left(\sqrt{.\overline{4}}\right)\pmf} + \dfrac{4}{.\overline{4}}$ Steve Wilson, 5/24Lawrence, KS 1710 (2.8) $\dfrac{4 + 4 - .4}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1711 (4.8) $\dfrac{.\overline{4} + (4! - .\overline{4}\%)\%}{4\%\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1712 (4.0) $\dfrac{4 - 4! \times 4!\pmf}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1713 (5.8) $\dfrac{\coth\ln 4 + (\coth\ln 4)\%}{\left(\sqrt{.\overline{4}}\right)\pmf} - 4$ Steve Wilson, 5/24Lawrence, KS 1714 (4.2) $\dfrac{4! - 4\pmf}{\left( \sqrt{\sqrt{4} - 4\%} \right)\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1715 (5.8) $\dfrac{\coth\ln 4}{\left(\sqrt{.\overline{4}}\right)\pmf} + \dfrac{\arcsec\sqrt{4}}{4^\circ}$ Steve Wilson, 5/24Lawrence, KS 1716 (4.6) $\dfrac{\sqrt{.\overline{4}} + 4! \times 4\pmf}{.\overline{4}\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1717 (5.8) $\dfrac{\coth\ln 4 + (\coth\ln 4)\%}{\left(\sqrt{.\overline{44}}\right)\pmf}$ Steve Wilson, 5/24Lawrence, KS 1718 (5.4) $\dfrac{\coth\ln\coth\arcosh\sqrt{4}}{4\pmf} - \sqrt[.4]{4}$ Steve Wilson, 5/24Lawrence, KS 1719 (5.8) $\dfrac{\coth\ln\coth\arcosh\sqrt{4}}{4\pmf} - \cosh(\sqrt{4} \times \arcosh 4)$ Steve Wilson, 5/24Lawrence, KS 1720 (3.6) $\dfrac{4}{4\pmf} + (4 + \sqrt{4})!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1721 (5.8) $\dfrac{\coth\ln 4 - (\sqrt{4})\pmf}{\left(\sqrt{.\overline{4}}\right)\pmf} + 4!$ Steve Wilson, 5/24Lawrence, KS 1722 (5.6) $\dfrac{\coth\ln 4}{\left(\sqrt{.\overline{4}}\right)\pmf} - 4! + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1723 (5.8) $\dfrac{\cot\arctan(4\%) - \sqrt{4}}{(\csch\ln\sqrt{4})\%} - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1724 (4.2) $\sqrt{\sqrt{\sqrt{\left( \dfrac{4!}{\sqrt{4}} \right)^{4!}}}} - 4$ Steve Wilson, 11/09Raytown, MO 1725 (4.4) $\dfrac{\sqrt{.\overline{4}} + \dfrac{.4}{4}}{.\overline{4}\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1726 (4.2) $\dfrac{4 + \sqrt{4\%}}{4!\%\%} - 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1727 (5.8) $\dfrac{\cot\arctan(4\%) - \sqrt{4}}{(\csch\ln\sqrt{4})\%} + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1728 (3.6) $(4 \times 4! - 4!) \times 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1729 (5.6) $\dfrac{\cot\arctan(4\%) - \sqrt{4}}{(\csch\ln\sqrt{4})\%} + 4$ Steve Wilson, 5/24Lawrence, KS 1730 (4.2) $\dfrac{4 - \dfrac{4!\%}{.\overline{4}}}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1731 (5.8) $\dfrac{\coth\ln 4}{\left(\sqrt{.\overline{4}}\right)\pmf} + \cosh(\sqrt{4} \times \arcosh 4)$ Steve Wilson, 5/24Lawrence, KS 1732 (4.2) $\sqrt{\sqrt{\sqrt{\left( \dfrac{4!}{\sqrt{4}} \right)^{4!}}}} + 4$ Steve Wilson, 11/09Raytown, MO 1733 (5.8) $\dfrac{\coth\ln 4}{\left(\sqrt{.\overline{4}}\right)\pmf} + \cosh(\sqrt{4} \times \arsinh 4)$ Steve Wilson, 5/24Lawrence, KS 1734 (4.2) $\sqrt{\left(\dfrac{\sqrt{4} + 4\%}{(\sqrt{4!})\%} \right)^4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1735 (4.4) $\sqrt{4!\pm^{-4}}\phantom8 - \dfrac{.\overline{4}}{.4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1736 (4.2) $\sqrt{4!\pm^{-4}}\phantom8 - \dfrac{.\overline{4}}{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1737 (4.2) $\left( 4\%^{-4}\% + \sqrt{4} \right) \times .\overline{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1738 (5.6) $\dfrac{\coth\ln\coth\arcosh\sqrt{4}}{4\pmf} - \dfrac{4!}{\sqrt{4}}$ Steve Wilson, 5/24Lawrence, KS 1739 (5.4) $\dfrac{\coth\ln\coth\arcosh\sqrt{4} - 44\pmf}{4\pmf}$ Steve Wilson, 5/24Lawrence, KS 1740 (3.8) $\dfrac{(4 + \sqrt{4})! - 4!}{.4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1741 (5.6) $\dfrac{\coth\ln\coth\arcosh\sqrt{4}}{4\pmf} - \dfrac{4}{.\overline{4}}$ Steve Wilson, 5/24Lawrence, KS 1742 (5.2) $\dfrac{\coth\ln\coth\arcosh\sqrt{4}}{4\pmf} - 4 - 4$ Steve Wilson, 5/24Lawrence, KS 1743 (5.6) $\dfrac{\coth\ln\coth\arcosh\sqrt{4} - (4! + 4)\pmf}{4\pmf}$ Steve Wilson, 5/24Lawrence, KS 1744 (3.8) $\sqrt[\sqrt{4\%}]{4} + (4 + \sqrt{4})!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1745 (5.6) $\dfrac{\coth\ln\coth\arcosh\sqrt{4}}{4\pmf} - \dfrac{\sqrt{4}}{.4}$ Steve Wilson, 5/24Lawrence, KS 1746 (4.0) $\dfrac{4 + 4 - 4!\%}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1747 (5.6) $\dfrac{\coth\ln\coth\arcosh\sqrt{4}}{4\pmf} - \log\left(\dfrac{4}{4\pmf}\right)$ Steve Wilson, 6/24Lawrence, KS 1748 (4.2) $\dfrac{4 + \sqrt{4\%}}{4!\%\%} - \sqrt{4}$ Steve Wilson, 11/09Raytown, MO 1749 (5.2) $\dfrac{\coth\ln\coth\arcosh\sqrt{4}}{4\pmf} - \dfrac44$ Steve Wilson, 5/24Lawrence, KS 1750 (3.4) $\dfrac{4! + 4}{4 \times 4\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1751 (5.2) $\dfrac{\coth\ln\coth\arcosh\sqrt{4}}{4\pmf} + \dfrac44$ Steve Wilson, 5/24Lawrence, KS 1752 (4.0) $\left( \dfrac{4}{.\overline{4}\%} - 4! \right) \times \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1753 (5.6) $\dfrac{\coth\ln\coth\arcosh\sqrt{4}}{4\pmf} + \log\left(\dfrac{4}{4\pmf}\right)$ Steve Wilson, 6/24Lawrence, KS 1754 (4.0) $\dfrac{4 + \sqrt{4\%}}{4!\%\%} + 4$ Steve Wilson, 11/09Raytown, MO 1755 (4.0) $\dfrac{4 + 4 - \sqrt{4\%}}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1756 (4.2) $\dfrac{\sqrt{.\overline{4}}}{.\overline{4}\pmf} + 4^4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1757 (5.6) $\dfrac{\coth\ln\coth\arcosh\sqrt{4} + (4! + 4)\pmf}{4\pmf}$ Steve Wilson, 5/24Lawrence, KS 1758 (5.6) $\dfrac{\coth\ln 4 + 4\%}{\left(\sqrt{.\overline{4}}\right)\pmf} - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1759 (5.6) $\dfrac{\coth\ln\coth\arcosh\sqrt{4}}{4\pmf} + \dfrac{4}{.\overline{4}}$ Steve Wilson, 5/24Lawrence, KS 1760 (3.8) $\dfrac{4.4}{\left(\sqrt{\sqrt{4^{-4}}}\right)\%}$ Steve Wilson, 11/09Raytown, MO 1761 (5.4) $\dfrac{\coth\ln\coth\arcosh\sqrt{4} + 44\pmf}{4\pmf}$ Steve Wilson, 5/24Lawrence, KS 1762 (5.6) $\dfrac{\coth\ln 4 + 4\%}{\left(\sqrt{.\overline{4}}\right)\pmf} + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1763 (5.6) $\coth\ln\coth\arcsch(4\%) + \sqrt{4^{4/.\overline{4}}}$ Steve Wilson, 5/24Lawrence, KS 1764 (3.4) $\sqrt{(44 - \sqrt{4})^4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1765 (4.2) $\dfrac{4 + (4! - .4)\%}{4!\%\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1766 (5.2) $\dfrac{4! - .4}{(\csch\ln\sqrt{4})\%} - 4$ Steve Wilson, 5/24Lawrence, KS 1767 (5.2) $\dfrac{4! - 44\%}{(\csch\ln\sqrt{4})\%}$ Steve Wilson, 5/24Lawrence, KS 1768 (5.2) $\dfrac{4!}{(\csch\ln\sqrt{4})\%} - \sqrt[.4]{4}$ Steve Wilson, 5/24Lawrence, KS 1769 (5.6) $\dfrac{4!}{(\csch\ln\sqrt{4})\%} - \cosh(\sqrt{4} \times \arcosh 4)$ Steve Wilson, 5/24Lawrence, KS 1770 (4.2) $\dfrac{4! - .4}{\left(\sqrt{4 \times .\overline{4}} \right)\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1771 (5.2) $\dfrac{\sinh\ln\sqrt{4} - 4\%}{4\%\%} - 4$ Steve Wilson, 5/24Lawrence, KS 1772 (5.2) $\dfrac{4!}{(\csch\ln\sqrt{4})\%} - 4! - 4$ Steve Wilson, 5/24Lawrence, KS 1773 (5.4) $\dfrac{\sinh\ln\sqrt{4} - 4\%}{4\%\%} - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1774 (4.2) $\dfrac{4 + \sqrt{4\%}}{4!\%\%} + 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1775 (4.2) $\dfrac{4 - \dfrac{\sqrt{4\%}}{.\overline{4}}}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1776 (2.0) $444 \times 4$ Darren Boss, 2/03Shawnee, KS 1777 (5.4) $\dfrac{\sinh\ln\sqrt{4} - 4\%}{4\%\%} + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1778 (4.4) $\dfrac{4 - .\overline{4} + .\overline{4}\pmf}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1779 (5.2) $\dfrac{\sinh\ln\sqrt{4} - 4\%}{4\%\%} + 4$ Steve Wilson, 5/24Lawrence, KS 1780 (3.6) $\dfrac{4 - 44\%}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1781 (5.4) $\dfrac{4! - \sqrt{4\%}}{(\csch\ln\sqrt{4})\%} - 4$ Steve Wilson, 5/24Lawrence, KS 1782 (4.0) $(4 - 4\%) \times \dfrac{\sqrt{4}}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1783 (5.6) $\dfrac{4! - \sqrt{4\%}}{(\csch\ln\sqrt{4})\%} - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1784 (3.8) $4 \times \left( \dfrac{\sqrt{4}}{.\overline{4}\%} - 4 \right)$ Paolo Pellegrini, 10/09Martina Franca, Italy 1785 (4.4) $\dfrac{4! - \sqrt{4\%}}{\left(\sqrt{4 \times .\overline{4}} \right)\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1786 (5.4) $\dfrac{4!}{(\csch\ln\sqrt{4})\%} - (\antilog 4)\pm - 4$ Steve Wilson, 5/24Lawrence, KS 1787 (5.6) $\dfrac{4! - \sqrt{4\%}}{(\csch\ln\sqrt{4})\%} + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1788 (4.0) $\dfrac{4 - .4 - 4!\pmf}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1789 (5.4) $\dfrac{4! - \sqrt{4\%}}{(\csch\ln\sqrt{4})\%} + 4$ Steve Wilson, 5/24Lawrence, KS 1790 (3.6) $\dfrac{(4 + \sqrt{4})! - 4}{.4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1791 (2.8) $\dfrac{4 + 4 - 4\%}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1792 (3.6) $(4 + 4)! \times 4.\overline{4}\%$ Paolo Pellegrini, 10/09Martina Franca, Italy 1793 (5.2) $\dfrac{4! - 4\%}{(\csch\ln\sqrt{4})\%} - 4$ Steve Wilson, 5/24Lawrence, KS 1794 (4.2) $\dfrac{\dfrac{4!}{(\sqrt{4})\%} - 4}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1795 (3.8) $\dfrac{(4 + \sqrt{4})! - \sqrt{4}}{.4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1796 (2.6) $\dfrac{4 + 4}{.\overline{4}\%} - 4$ Steve Wilson, 11/09Raytown, MO 1797 (4.2) $\dfrac{4! - 4\%}{\left( \sqrt{4 \times .\overline{4}} \right)\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1798 (3.8) $\dfrac{4 + 4}{.\overline{4}\%} - \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1799 (3.8) $\dfrac{(4 + \sqrt{4})! - .4}{.4}$ Steve Wilson, 11/09Raytown, MO 1800 (2.6) $\dfrac{4 + 4}{.\overline{44}\%}$ David Barksdale, 3/09Kirkland, WA 1801 (3.8) $\dfrac{(4 + \sqrt{4})! + .4}{.4}$ Steve Wilson, 11/09Raytown, MO 1802 (3.8) $\dfrac{4 + 4}{.\overline{4}\%} + \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1803 (4.2) $\dfrac{4! + 4\%}{\left(\sqrt{4 \times .\overline{4}}\right)\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1804 (2.6) $\dfrac{4 + 4}{.\overline{4}\%} + 4$ Steve Wilson, 11/09Raytown, MO 1805 (3.8) $\dfrac{(4 + \sqrt{4})! + \sqrt{4}}{.4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1806 (4.2) $\dfrac{\dfrac{4!}{(\sqrt{4})\%} + 4}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1807 (5.2) $\dfrac{4! + 4\%}{(\csch\ln\sqrt{4})\%} + 4$ Steve Wilson, 5/24Lawrence, KS 1808 (3.8) $\left( \dfrac{4}{.\overline{4}\%} + 4 \right) \times \sqrt{4}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1809 (2.8) $\dfrac{4 + 4 + 4\%}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1810 (3.6) $\dfrac{(4 + \sqrt{4})! + 4}{.4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1811 (5.4) $\dfrac{4! + \sqrt{4\%}}{(\csch\ln\sqrt{4})\%} - 4$ Steve Wilson, 5/24Lawrence, KS 1812 (4.0) $\dfrac{4 - .4 + 4!\pmf}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1813 (5.6) $\dfrac{4! + \sqrt{4\%}}{(\csch\ln\sqrt{4})\%} - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1814 (4.0) $\dfrac{\left(\dfrac{4}{.4} \right)!\pmf}{\sqrt{4}} - .4$ Steve Wilson, 11/09Raytown, MO 1815 (4.4) $\dfrac{4! + \sqrt{4\%}}{\left(\sqrt{4 \times .\overline{4}} \right)\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1816 (3.8) $4 \times \left( \dfrac{\sqrt{4}}{.\overline{4}\%} + 4 \right)$ Paolo Pellegrini, 10/09Martina Franca, Italy 1817 (5.6) $\dfrac{4! + \sqrt{4\%}}{(\csch\ln\sqrt{4})\%} + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1818 (4.0) $(4 + 4\%) \times \dfrac{\sqrt{4}}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1819 (5.4) $\dfrac{4! + \sqrt{4\%}}{(\csch\ln\sqrt{4})\%} + 4$ Steve Wilson, 5/24Lawrence, KS 1820 (3.8) $\dfrac{4 - .4 + 4\%}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1821 (4.4) $\dfrac{\dfrac{\sqrt{4}}{4!\%\%} - 4!}{.\overline{4}}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1822 (5.4) $\dfrac{4!}{(\csch\ln\sqrt{4})\%} + 4! - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1823 (5.0) $\cosh(4 \times \arcosh 4) - \antilog\sqrt{4} + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1824 (3.8) $\dfrac{4 + 4}{.\overline{4}\%} + 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1825 (3.8) $\dfrac{44 - \sqrt{4\%}}{4!\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1826 (4.8) $\dfrac{.\overline{4} - .\overline{4}\pmf}{4!\%\pmf} - 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1827 (5.4) $\dfrac{\sinh\ln\sqrt{4}}{4\%\%} - 4! - 4!$ Steve Wilson, 5/24Lawrence, KS 1828 (5.2) $\dfrac{4!}{(\csch\ln\sqrt{4})\%} + 4! + 4$ Steve Wilson, 5/24Lawrence, KS 1829 (5.4) $\dfrac{4! - .4}{.4 \times \tanh\ln\coth\arcosh 4}$ Steve Wilson, 5/24Lawrence, KS 1830 (4.2) $\dfrac{4! + .4}{\left(\sqrt{4 \times .\overline{4}} \right)\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1831 (5.0) $\dfrac{\sinh\ln\sqrt{4}}{4\%\%} - 44$ Steve Wilson, 5/24Lawrence, KS 1832 (5.2) $\dfrac{4!}{(\csch\ln\sqrt{4})\%} + \sqrt[.4]{4}$ Steve Wilson, 5/24Lawrence, KS 1833 (5.2) $\dfrac{4! + 44\%}{(\csch\ln\sqrt{4})\%}$ Steve Wilson, 5/24Lawrence, KS 1834 (4.0) $\dfrac{44}{4!\pmf} + \sqrt{.\overline{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1835 (3.6) $\dfrac{44 + 4\%}{4!\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1836 (4.0) $\dfrac{4 \times (\sqrt{4} + 4\%)}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1837 (5.8) $\dfrac{4!}{(\csch\ln\sqrt{4})\%} + \coth\ln\coth\arsinh 4 + 4$ Steve Wilson, 5/24Lawrence, KS 1838 (5.8) $\dfrac{\sinh\ln\sqrt{4}}{4\%\%} - \coth\ln\coth\arsinh 4 - 4$ Steve Wilson, 5/24Lawrence, KS 1839 (5.6) $\dfrac{4! + \sqrt{4\%}}{(\csch\ln\sqrt{4})\%} + 4!$ Steve Wilson, 5/24Lawrence, KS 1840 (3.8) $\dfrac{4 - (\sqrt[.4]{4})\%}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1841 (5.6) $\dfrac{\sinh\ln\sqrt{4}}{4\%\%} - 4! - (\antilog 4)\pm$ Steve Wilson, 5/24Lawrence, KS 1842 (5.6) $\dfrac{4! + 4!\%}{(\csch\ln\sqrt{4})\%} + 4!$ Steve Wilson, 5/24Lawrence, KS 1843 (5.2) $\dfrac{\sinh\ln\sqrt{4}}{4\%\%} - \sqrt[.4]{4}$ Steve Wilson, 5/24Lawrence, KS 1844 (5.0) $\dfrac{4!}{(\csch\ln\sqrt{4})\%} + 44$ Steve Wilson, 5/24Lawrence, KS 1845 (4.0) $\dfrac{4 + 4 + \sqrt{4\%}}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1846 (4.6) $\dfrac{.\overline{4} - .\overline{4}\pmf}{4!\%\pmf} - 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1847 (5.2) $\dfrac{\sinh\ln\sqrt{4}}{4\%\%} - 4! - 4$ Steve Wilson, 5/24Lawrence, KS 1848 (4.0) $\left( \dfrac{4}{.\overline{4}\%} + 4! \right) \times \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1849 (4.2) $\sqrt{\left(\dfrac{\sqrt{4}}{.\overline{4}\%} - \sqrt{4} \right)^4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1850 (3.4) $\dfrac{44.4}{4!\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1851 (4.4) $\dfrac{\sqrt{4}}{\left( .4 + \sqrt{.\overline{4}} \right)\pmf} - 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1852 (4.8) $\dfrac{.\overline{4} - .\overline{4}\pmf}{4!\%\pmf} + \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1853 (5.4) $\dfrac{\sinh\ln\sqrt{4}}{4\%\%} - 4! + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1854 (4.0) $\dfrac{4 + 4 + 4!\%}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1855 (5.2) $\dfrac{\sinh\ln\sqrt{4} - (4 + 4)\pmf}{4\%\%}$ Steve Wilson, 5/24Lawrence, KS 1856 (4.0) $\dfrac{4 - 4!\%}{(\sqrt{4})\pmf} - 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1857 (5.8) $\dfrac{\sinh\ln\sqrt{4}}{4\%\%} - \dfrac{4!}{\csch\ln\sqrt{4}}$ Steve Wilson, 5/24Lawrence, KS 1858 (5.8) $\dfrac{\sinh\ln\sqrt{4}}{4\%\%} - \cosh(4 \times \arcosh\sqrt{\sqrt{4}})$ Steve Wilson, 5/24Lawrence, KS 1859 (5.0) $\dfrac{\sinh\ln\sqrt{4}}{4\%\%} - 4 \times 4$ Steve Wilson, 5/24Lawrence, KS 1860 (3.8) $\dfrac{4 - (4! + 4)\%}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1861 (4.8) $\cosh(4 \times \arcosh 4) - \dfrac{4!}{.4}$ Steve Wilson, 5/24Lawrence, KS 1862 (5.8) $\dfrac{\antilog\sqrt{4} - \sqrt{4}}{\tanh\ln\sqrt{\dfrac{.\overline{4}}{.4}}}$ Steve Wilson, 5/24Lawrence, KS 1863 (5.4) $\dfrac{\sinh\ln\sqrt{4} - 4\pmf}{4\%\%} - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1864 (5.2) $\dfrac{\sinh\ln\sqrt{4} - 4.4\pmf}{4\%\%}$ Steve Wilson, 5/24Lawrence, KS 1865 (4.6) $\dfrac{\dfrac{\sqrt{4}}{.\overline{4}} - 4!\pmf}{4!\%\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1866 (4.2) $\dfrac{\dfrac{\sqrt{4}}{4!\%\%} - 4}{.\overline{4}}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1867 (5.4) $\dfrac{\sinh\ln\sqrt{4} - 4\pmf}{4\%\%} + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1868 (4.2) $\dfrac{4 - 4!\% - 4!\pmf}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1869 (5.2) $\dfrac{\sinh\ln\sqrt{4}}{4\%\%} - \dfrac{4!}{4}$ Steve Wilson, 5/24Lawrence, KS 1870 (4.0) $\dfrac{4 - (4! + \sqrt{4})\%}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1871 (4.2) $\dfrac{\sqrt{4}}{\left(.4 + \sqrt{.\overline{4}} \right)\pmf} - 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1872 (3.6) $\dfrac{4 - 4^4\pmf}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1873 (4.4) $\dfrac{\sqrt{4}}{\left(.4 + \sqrt{.\overline{4}} \right)\pmf} - \sqrt{4}$ Steve Wilson, 11/09Raytown, MO 1874 (4.4) $\dfrac{\dfrac{\sqrt{4}}{.\overline{4}\%\%} - 4!}{4!}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1875 (3.8) $4! \times \sqrt{4} \times .4^{-4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1876 (3.8) $\dfrac{4 - 4!\%}{(\sqrt{4})\pmf} - 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1877 (4.4) $\dfrac{\sqrt{4}}{\left(.4 + \sqrt{.\overline{4}} \right)\pmf} + \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1878 (4.0) $\dfrac{4 - 4!\% - 4\pmf}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1879 (4.2) $\dfrac{\sqrt{4}}{\left(.4 + \sqrt{.\overline{4}} \right)\pmf} + 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1880 (3.8) $(4 - 4!\%) \times \dfrac{\sqrt{4}}{4\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1881 (4.2) $\dfrac{4 - (4! - \sqrt{4\%})\%}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1882 (4.0) $\dfrac{4 - 4!\% + 4\pmf}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1883 (5.4) $\dfrac{\sinh\ln\sqrt{4} + 4\pmf}{4\%\%} - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1884 (3.8) $\dfrac{4 - 4!\%}{(\sqrt{4})\pmf} + 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1885 (4.6) $\dfrac{\left( \dfrac{\sqrt{4}}{.\overline{4}\pmf} + 4! \right)\%}{4!\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1886 (5.2) $\dfrac{\sinh\ln\sqrt{4} + 4.4\pmf}{4\%\%}$ Steve Wilson, 5/24Lawrence, KS 1887 (5.4) $\dfrac{\sinh\ln\sqrt{4} + 4\pmf}{4\%\%} + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1888 (4.6) $\dfrac{(4! - .4)\%}{\left( \sqrt[-\sqrt{.\overline{4}}]{4} \right)\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1889 (4.6) $\cosh(4 \times \arcosh 4) - \sqrt[.4]{4}$ Steve Wilson, 5/24Lawrence, KS 1890 (2.6) $\dfrac{4.4 + 4}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1891 (4.4) $\dfrac{.\overline{4} + .4 - 4\pmf}{.\overline{4}\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1892 (4.2) $\dfrac{4 - 4!\% + 4!\pmf}{(\sqrt{4})\pmf}$ Steve Wilson, 5/10Raytown, MO 1893 (4.6) $\cosh(4 \times \arcosh 4) - 4! - 4$ Steve Wilson, 9/23Lawrence, KS 1894 (5.2) $\cosh(4 \times \arcosh 4) - \cot\arctan(4\%) - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1895 (4.8) $\cosh(4 \times \arcosh 4) - 4! - \sqrt{4}$ Steve Wilson, 9/23Lawrence, KS 1896 (4.0) $4 \times \left( \dfrac{\sqrt{4}}{.\overline{4}\%} + 4! \right)$ Steve Wilson, 5/10Raytown, MO 1897 (4.8) $\cosh(4 \times \arcosh 4) - (\sqrt{4 \times 4})!$ Steve Wilson, 9/23Lawrence, KS 1898 (4.0) $\dfrac{4 - \sqrt{4\%} - 4\pmf}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1899 (4.2) $\dfrac{4 - \sqrt{4\%} - (\sqrt{4})\pmf}{(\sqrt{4})\pmf}$ Steve Wilson, 5/10Raytown, MO 1900 (2.6) $\dfrac{4 + 4 - .4}{.4\%}$ Steve Wilson, 11/09Raytown, MO 1901 (4.2) $\dfrac{4 - \sqrt{4\%} + (\sqrt{4})\pmf}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1902 (4.0) $\dfrac{4 - \sqrt{4\%} + 4\pmf}{(\sqrt{4})\pmf}$ Steve Wilson, 11/09Raytown, MO 1903 (5.2) $\dfrac{\sinh\ln\sqrt{4}}{4\%\%} + 4! + 4$ Steve Wilson, 5/24Lawrence, KS 1904 (3.6) $4 \times \left( \dfrac{\sqrt{4}}{4\pmf} - 4! \right)$ Paolo Pellegrini, 10/09Martina Franca, Italy 1905 (4.4) $\cosh(4 \times \arcosh 4) - 4 \times 4$ Steve Wilson, 9/23Lawrence, KS 1906 (5.0) $\cosh(4 \times \arcosh 4) - \dfrac{\arcsec\sqrt{4}}{4^\circ}$ Steve Wilson, 5/24Lawrence, KS 1907 (4.8) $\cosh(4 \times \arcosh 4) - (\antilog 4)\pm - 4$ Steve Wilson, 5/24Lawrence, KS 1908 (4.2) $(4 + 4!\pm) \times \dfrac{\sqrt{4}}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1909 (4.4) $\dfrac{.\overline{4} + .4 + 4\pmf}{.\overline{4}\pmf}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1910 (4.4) $\dfrac{.\overline{4} \times \sqrt{4} - 4\%}{.\overline{4}\pmf}$ Steve Wilson, 11/09Raytown, MO 1911 (4.6) $\cosh(4 \times \arcosh 4) - \dfrac{4}{.4}$ Steve Wilson, 9/23Lawrence, KS 1912 (3.4) $\sqrt{44^4} - 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1913 (4.4) $\cosh(4 \times \arcosh 4) - 4 - 4$ Steve Wilson, 9/23Lawrence, KS 1914 (5.2) $\cosh(4 \times \arcosh 4) - \cosh(\sqrt{4} \times \arcosh\sqrt{4})$ Steve Wilson, 5/24Lawrence, KS 1915 (4.6) $\cosh(4 \times \arcosh 4) - \dfrac{4!}{4}$ Steve Wilson, 9/23Lawrence, KS 1916 (4.0) $\dfrac{(4 + 4)!\pm - \sqrt{4}\phantom8}{(\sqrt{4}) \%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1917 (4.6) $\cosh(4 \times \arcosh 4) - \sqrt{4 \times 4}$ Steve Wilson, 9/23Lawrence, KS 1918 (4.6) $\dfrac{4!\%}{\left(\sqrt[-\sqrt{.\overline{4}}]{4} \right)\pmf} - \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1919 (4.6) $\cosh(4 \times \arcosh 4) - \dfrac{4}{\sqrt{4}}$ Steve Wilson, 9/23Lawrence, KS 1920 (3.4) $(4! - 4) \times 4 \times 4!$ Paolo Pellegrini, 10/09Martina Franca, Italy 1921 (4.4) $\dfrac44 \times \cosh(4 \times \arcosh 4)$ Steve Wilson, 9/23Lawrence, KS 1922 (4.4) $\cosh(4 \times \arcosh 4) + \dfrac44$ Steve Wilson, 9/23Lawrence, KS 1923 (4.6) $\cosh(4 \times \arcosh 4) + \dfrac{4}{\sqrt{4}}$ Steve Wilson, 9/23Lawrence, KS 1924 (4.0) $\sqrt[\sqrt{4\%}]{4} + \dfrac{4}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1925 (3.4) $\dfrac{\dfrac{4}{.\overline{4}} - .\overline{4}}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1926 (4.8) $\cosh(4 \times \arcosh 4) + \dfrac{\sqrt{4}}{.4}$ Steve Wilson, 9/23Lawrence, KS 1927 (4.6) $\cosh(4 \times \arcosh 4) + \dfrac{4!}{4}$ Steve Wilson, 9/23Lawrence, KS 1928 (5.2) $\cosh(4 \times \arcosh 4) + \cosh(\sqrt{4} \times \arcosh\sqrt{4})$ Steve Wilson, 5/24Lawrence, KS 1929 (4.4) $4 \times \left( \left( \sqrt{.\overline{4}\%^{-4}} \right) \% -4! \right)$ Paolo Pellegrini, 10/09Martina Franca, Italy 1930 (4.8) $\cosh(4 \times \arcosh 4) + \dfrac{4}{.\overline{4}}$ Steve Wilson, 9/23Lawrence, KS 1931 (4.6) $\cosh(4 \times \arcosh 4) + \dfrac{4}{.4}$ Steve Wilson, 9/23Lawrence, KS 1932 (3.2) $\sqrt{44^4} - 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1933 (4.8) $\cosh(4 \times \arcosh 4) + \dfrac{4!}{\sqrt{4}}$ Steve Wilson, 9/23Lawrence, KS 1934 (3.4) $\sqrt{44^4} - \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1935 (3.2) $\dfrac{\dfrac{4}{.\overline{4}} - .4}{.\overline{4}\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1936 (2.0) $44 \times 44$ Steve Barker, 1/03Stilwell, KS 1937 (4.4) $\cosh(4 \times \arcosh 4) + 4 \times 4$ Steve Wilson, 9/23Lawrence, KS 1938 (3.4) $\sqrt{44^4} + \sqrt{4}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1939 (5.2) $\cosh(4 \times \arcosh 4) + \dfrac{4!}{\sech\ln\sqrt{4}}$ Steve Wilson, 5/24Lawrence, KS 1940 (3.2) $\sqrt{44^4} + 4$ Paolo Pellegrini, 10/09Martina Franca, Italy 1941 (4.6) $\cosh(4 \times \arcosh 4) + 4! - 4$ Steve Wilson, 9/23Lawrence, KS 1942 (5.0) $\cosh(4 \times \arcosh 4) + \cot\arctan(4\%) - 4$ Steve Wilson, 5/24Lawrence, KS 1943 (4.8) $\cosh(4 \times \arcosh 4) + 4! - \sqrt{4}$ Steve Wilson, 9/23Lawrence, KS 1944 (3.8) $4^4 \times \sqrt[-.4]{.\overline{4}}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1945 (4.8) $\cosh(4 \times \arcosh 4) + (\sqrt{4 \times 4})!$ Steve Wilson, 9/23Lawrence, KS 1946 (4.0) $\dfrac{4}{(\sqrt{4})\pmf} - \dfrac{4!}{.\overline{4}}$ Steve Wilson, 11/09Raytown, MO 1947 (4.8) $\cosh(4 \times \arcosh 4) + 4! + \sqrt{4}$ Steve Wilson, 9/23Lawrence, KS 1948 (4.4) $\dfrac{\left( \sqrt{\sqrt{4^{4!}}}\right)\% - \sqrt{4}}{(\sqrt{4})\%}$ Paolo Pellegrini, 10/09Martina Franca, Italy 1949 (4.6) $\cosh(4 \times \arcosh 4) + 4! + 4$ Steve Wilson, 9/23Lawrence, KS 1950 (3.8) $\dfrac{4}{(\sqrt{4})\pmf} - \dfrac{\sqrt{4}}{4\%}$ Steve Wilson, 11/09Raytown, MO 1951 (5.2) $\cosh(4 \times \arcosh 4) + \sqrt{\dfrac{4}{.\overline{4}\%}}$ Steve Wilson, 5/24Lawrence, KS 1952 (3.8) $\dfrac{4}{(\sqrt{4})\pmf} - 4! - 4!$ Steve Wilson, 11/09Raytown, MO 1953 (4.6) $\cosh(4 \times \arcosh 4) + \sqrt[.4]{4}$ Steve Wilson, 5/24Lawrence, KS 1954 (5.0) $\cosh(4 \times \arcosh 4) + \cosh(\sqrt{4} \times \arsinh 4)$ Steve Wilson, 5/24Lawrence, KS 1955 (4.0) $\dfrac{4 - \dfrac{4\%}{.\overline{4}}}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1956 (3.4) $\dfrac{4}{(\sqrt{4})\pmf} - 44$ Steve Wilson, 11/09Raytown, MO 1957 (5.2) $\cosh(4 \times \arcosh 4) + \dfrac{4!}{\sqrt{.\overline{4}}}$ Steve Wilson, 5/24Lawrence, KS 1958 (5.2) $\cosh(4 \times \arcosh 4) + \coth\ln\coth\arsinh 4 + 4$ Steve Wilson, 5/24Lawrence, KS 1959 (5.8) $\cosh(4 \times \arcosh 4) + \cot\arctan((\cot\arctan(.4))\%) - \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1960 (3.4) $\sqrt{44^4} + 4!$ Steve Wilson, 11/09Raytown, MO 1961 (4.8) $\cosh(4 \times \arcosh 4) + (\antilog 4) \times 4\pm$ Steve Wilson, 5/24Lawrence, KS 1962 (5.8) $\dfrac{4}{\left(\sqrt{4}\right)\pmf} - \cot\arctan((\cot\arctan(.4))\%) + \sqrt{4}$ Steve Wilson, 5/24Lawrence, KS 1963 (5.2) $\dfrac{4}{\left(\sqrt{4}\right)\pmf} - \coth\ln\coth\arsinh 4 - 4$ Steve Wilson, 5/24Lawrence, KS 1964 (4.0) $\dfrac{4 - 4!\pmf}{(\sqrt{4})\pmf} - 4!$ Paolo Pellegrini, 5/10Martina Franca, Italy 1965 (4.4) $\dfrac{ \left(4 + \dfrac{\sqrt{4}}{4!\pmf} \right)\%}{.\overline{4}\pmf}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1966 (4.0) $\dfrac{4 - (\sqrt{4})\%}{(\sqrt{4})\pmf} - 4!$ Paolo Pellegrini, 5/10Martina Franca, Italy 1967 (5.0) $\dfrac{4}{\left(\sqrt{4}\right)\pmf} - \cosh(\sqrt{4} \times \arsinh 4)$ Steve Wilson, 5/24Lawrence, KS 1968 (3.6) $\dfrac{4}{(\sqrt{4})\pmf} - \sqrt[.4]{4}$ Steve Wilson, 11/09Raytown, MO 1969 (4.8) $\cosh(4 \times \arcosh 4) + 4! + 4!$ Steve Wilson, 5/24Lawrence, KS 1970 (3.8) $\dfrac{4 - \dfrac{4!\%}{4}}{(\sqrt{4})\pmf}$ Steve Wilson, 11/09Raytown, MO 1971 (4.2) $\dfrac{\dfrac{4}{.\overline{4}\%} - 4!}{.\overline{4}}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1972 (3.6) $\dfrac{4}{(\sqrt{4})\pmf} - 4! - 4$ Steve Wilson, 11/09Raytown, MO 1973 (4.2) $\dfrac{4 - \dfrac{4!\pmf}{.\overline{4}}}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1974 (3.8) $\dfrac{4}{(\sqrt{4})\pmf} - 4! - \sqrt{4}$ Steve Wilson, 11/09Raytown, MO 1975 (3.8) $\dfrac{4 - \dfrac{\sqrt{4\%}}{4}}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1976 (3.4) $\dfrac{4 + 4}{4\pmf} - 4!$ Steve Wilson, 11/09Raytown, MO 1977 (4.0) $\dfrac{4 + (\sqrt{4})\pmf}{(\sqrt{4})\pmf} - 4!$ Paolo Pellegrini, 5/10Martina Franca, Italy 1978 (3.8) $\dfrac{4}{(\sqrt{4})\pmf} - 4! + \sqrt{4}$ Steve Wilson, 11/09Raytown, MO 1979 (4.0) $\dfrac{4 - (4 + \sqrt{4\%})\%}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1980 (3.6) $\dfrac{4}{(\sqrt{4})\pmf} - 4! + 4$ Steve Wilson, 11/09Raytown, MO 1981 (4.0) $\dfrac{4 - (4 - \sqrt{4\%})\%}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1982 (3.8) $\dfrac{4 - 4\%}{(\sqrt{4})\pmf} + \sqrt{4}$ Steve Wilson, 11/09Raytown, MO 1983 (5.2) $\dfrac{4}{\left(\sqrt{4}\right)\pmf} - \cosh(4 \times \arcosh\sqrt{\sqrt{4}})$ Steve Wilson, 5/24Lawrence, KS 1984 (3.4) $4 \times \left( \dfrac{\sqrt{4}}{4\pmf} - 4 \right)$ Steve Wilson, 11/09Raytown, MO 1985 (4.2) $\dfrac{4 - \left(\sqrt{\dfrac{4}{.\overline{4}}}\right)\%}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1986 (3.8) $\dfrac{4 - (\sqrt{4})\%}{(\sqrt{4})\pmf} - 4$ Steve Wilson, 11/09Raytown, MO 1987 (4.0) $\dfrac{4 - (4! + \sqrt{4})\pmf}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1988 (3.8) $\dfrac{4}{(\sqrt{4})\pmf} - \dfrac{4!}{\sqrt{4}}$ Steve Wilson, 11/09Raytown, MO 1989 (4.0) $\dfrac{4 - (4! - \sqrt{4})\pmf}{(\sqrt{4})\pmf}$ Paolo Pellegrini, 5/10Martina Franca, Italy 1990 (2.6) $\dfrac{4 + 4 - 4\%}{.4\%}$ Steve Wilson, 11/09Raytown, MO 1991 (3.8) $\dfrac{4}{(\sqrt{4})\pmf} - \dfrac{4}{.\overline{4}}$ Steve Wilson, 11/09Raytown, MO 1992 (3.4) $\dfrac{4}{(\sqrt{4})\pmf} - 4 - 4$ Steve Wilson, 11/09Raytown, MO 1993 (5.2) $\dfrac{4}{\left(\sqrt{4}\right)\pmf} - \cosh(\sqrt{4} \times \arcosh\sqrt{4})$ Steve Wilson, 5/24Lawrence, KS 1994 (3.6) $\dfrac{4}{(\sqrt{4})\pmf} - 4 - \sqrt{4}$ Steve Wilson, 11/09Raytown, MO 1995 (3.8) $\dfrac{4}{(\sqrt{4})\pmf} - \dfrac{\sqrt{4}}{.4}$ Steve Wilson, 11/09Raytown, MO 1996 (2.4) $\dfrac{4 + 4}{.4\%} - 4$ Steve Wilson, 11/09Raytown, MO 1997 (3.8) $\dfrac{4 + (\sqrt{4})\pmf}{(\sqrt{4})\pmf} - 4$ Paolo Pellegrini, 5/10Martina Franca, Italy 1998 (3.6) $\dfrac{4}{(\sqrt{4})\pmf} - 4 + \sqrt{4}$ Steve Wilson, 11/09Raytown, MO 1999 (2.8) $\dfrac{4 + 4 - .4\%}{.4\%}$ Steve Wilson, 11/09Raytown, MO 2000 (2.6) $\dfrac{4 \times 4}{(.4 + .4)\%}$ Steve Wilson, 11/09Raytown, MO