Getting the maximum and the minimum with now

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The cryptarithmetic equation involves finding the three-digit integer "NOW" such that when squared, it equals the expression (xxxxxxNOW)/1983. The discussion highlights that the solution was obtained through brute force methods. The key focus is on determining the minimum and maximum values of "NOW." The calculations reveal specific bounds for "NOW," emphasizing the importance of exploring all possible digit combinations to satisfy the equation while adhering to the constraints of decimal digits and no leading zeros. The brute force approach proves effective in identifying these limits.
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In the following cryptarithmetic equation, each of the x’s represent a decimal digit, whether same or different, and “NOW” represents a three digit positive integer with no leading zero. Each of N, O and W represent a decimal digit, whether same or different.

(N O W) * (N O W)
= (x x x x x x N O W)/1983

What are the respective minimum value and the maximum value of “NOW”?
 
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There are three values of NOW that satisfy the equation:
272: 272 * 272 == 146710272 / 1983
375: 375 * 375 == 278859375 / 1983
647: 647 * 647 == 830101647 / 1983
272 is the minimum and 647 is the maximum.
This was found by brute force.
 
Also found by Brute Force:
There are three solutions:
n=2 o=7 w=2 => now*now*1983=146710272
n=3 o=7 w=5 => now*now*1983=278859375
n=6 o=4 w=7 => now*now*1983=830101647

Thus, the minimum value for now is 272 and the maximum is 647.
 

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