Hard Arithmetic Puzzles

#1845: 4 _ 4 _ 9 _ 9 = 17 hard #1846: 4 _ 4 _ 9 _ 9 = 15 hard #1847: 4 _ 5 _ 2 _ 6 = 19 hard #1849: 4 _ 5 _ 2 _ 2 = 19 hard #1857: 4 _ 5 _ 2 _ 7 = 17 hard #1859: 4 _ 5 _ 2 _ 8 = 18 hard #1860: 4 _ 5 _ 2 _ 9 = 19 hard #1863: 4 _ 5 _ 3 _ 9 = 19 hard #1865: 4 _ 5 _ 3 _ 3 = 19 hard #1867: 4 _ 5 _ 4 _ 8 = 14 hard #1870: 4 _ 5 _ 4 _ 4 = 19 hard #1874: 4 _ 5 _ 6 _ 2 = 19 hard #1877: 4 _ 5 _ 6 _ 6 = 19 hard #1880: 4 _ 5 _ 7 _ 7 = 19 hard #1881: 4 _ 5 _ 8 _ 4 = 14 hard #1883: 4 _ 5 _ 8 _ 2 = 16 hard #1884: 4 _ 5 _ 8 _ 4 = 18 hard #1885: 4 _ 5 _ 8 _ 8 = 19 hard #1888: 4 _ 5 _ 9 _ 3 = 19 hard #1889: 4 _ 5 _ 9 _ 3 = 17 hard #1890: 4 _ 5 _ 9 _ 9 = 19 hard #1893: 4 _ 6 _ 2 _ 5 = 19 hard #1901: 4 _ 6 _ 3 _ 7 = 18 hard #1902: 4 _ 6 _ 3 _ 8 = 20 hard #1916: 4 _ 6 _ 3 _ 9 = 17 hard #1925: 4 _ 6 _ 4 _ 8 = 16 hard #1933: 4 _ 6 _ 5 _ 2 = 19 hard #1941: 4 _ 6 _ 6 _ 8 = 18 hard #1942: 4 _ 6 _ 6 _ 9 = 16 hard #1943: 4 _ 6 _ 7 _ 3 = 18 hard #1944: 4 _ 6 _ 8 _ 3 = 20 hard #1945: 4 _ 6 _ 8 _ 4 = 16 hard #1958: 4 _ 6 _ 8 _ 6 = 18 hard #1962: 4 _ 6 _ 8 _ 9 = 12 hard #1964: 4 _ 6 _ 8 _ 3 = 16 hard #1968: 4 _ 6 _ 9 _ 6 = 16 hard #1977: 4 _ 6 _ 9 _ 5 = 11 hard #1979: 4 _ 6 _ 9 _ 6 = 12 hard #1980: 4 _ 6 _ 9 _ 7 = 13 hard #1982: 4 _ 6 _ 9 _ 8 = 14 hard #1984: 4 _ 6 _ 9 _ 9 = 15 hard #1985: 4 _ 7 _ 2 _ 1 = 15 hard #1988: 4 _ 7 _ 2 _ 5 = 19 hard #1994: 4 _ 7 _ 3 _ 6 = 18 hard #1995: 4 _ 7 _ 4 _ 2 = 18 hard #1996: 4 _ 7 _ 4 _ 8 = 18 hard #1999: 4 _ 7 _ 5 _ 7 = 20 hard #2000: 4 _ 7 _ 6 _ 3 = 18 hard