goruby, 55 bytes

Result

WA

Code [DL]

50.times.map{a=(((8*gets.to_i+1)**(.5)-1)/2);a.to_i==a}

stdin

01010011
00000011
10101111
10111110
01111000
00010011
00001010
00101101
00000000
11100000
00010101
00001100
01011100
10001101
00100100
00101000
10100100
00001111
11010110
10100000
00110001
00000110
00000001
10001000
10010111
01000101
10100111
11010010
01011011
01000010
00110111
10111010
01101001
01100011
11010101
00001011
01000010
01001110
00011100
11110101
10011001
01010110
11100111
00101110
11111101
10000110
11101101
01011011
10101011
01010100

stdout

stderr

/volume/CODE:1: no .<digit> floating literal anymore; put 0 before dot
es.map{a=(((8*gets.to_i+1)**(.5)-1)/2);a.to_i==a}
                              ^
/volume/CODE:1: syntax error, unexpected '.'
es.map{a=(((8*gets.to_i+1)**(.5)-1)/2);a.to_i==a}
                              ^

strace