If
ERROR * ERROR = GRIEVANCE
What is the title of this puzzle?
The largest possible value of GRIEVANCE is 987654327,
so the largest possible value of ERROR is sqrt(987654327) = 31426
so E is 1 or 2 or 3.
Since R*R ends in E and E is 1 or 2 or 3, then E must be 1 (because no squares end in 2 or 3).
So R = 9.
Our multiplication is 199?9 * 199?9.
Largest possible value is 19989^2 = 399560121
Smallest possible value is 19909^2 = 396368281
So, G is 3 and I is 6 or 7 or 8
Might as well do all of the multiplications;
ERROR GRIEVANCE
19909 396368281 no good, because A = C
19929 397165041 a winner!
19939 397563721 no good, because I = N
19949 397962601 no good, because R = E
19959 398361681 no good, because I = C
19969 398760961 no good, because R = N
19979 399160441 no good, because R = I
19989 399560121 no good, because R = I
So
0123456789
NEOGCAVI?R
70 6570
IN VAIN
Full Solution (Spoiler)
