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70 6570 (Posted on 2016-01-14) Difficulty: 3 of 5
If

ERROR * ERROR = GRIEVANCE

What is the title of this puzzle?

See The Solution Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

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Solution Full Solution (Spoiler) Comment 2 of 2 |
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

  Posted by Steve Herman on 2016-01-14 12:59:18
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