Getting the maximum and the minimum with now

[K Sengupta]

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”?

 

[Jimmy Snyder]

Spoiler

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.

 

[Edgardo]

Also found by Brute Force:

Spoiler

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.