as smarter guys explained, using modulo arithmetic voodoo

Sorry. It's this quote:

The sum of the digits of a number are congruent to the number itself modulo 9. Thus, if A=B*k and A has the same digits as B, then A%9=((B%9)*k)%9.

from here: 

https://wlmb.github.io/2025/12/01/PWC350/
He is a scientist, so I trust him :-). E.g. for hex numbers:

my $m = 15;                             # max digit
for my $r ( 0 .. $m ) {                 # remainder
    print "$r:\t";
    for my $w ( 2 .. $m ) {             # witness
        if ( $r == ( $r * $w ) % $m ) {
            print "$w "
        }
    }
    print "\n"
}

# 0:      2 3 4 5 6 7 8 9 10 11 12 13 14 15
# 1:
# 2:
# 3:      6 11
# 4:
# 5:      4 7 10 13
# 6:      6 11
# 7:
# 8:
# 9:      6 11
# 10:     4 7 10 13
# 11:
# 12:     6 11
# 13:
# 14:
# 15:

[download]

Easy to see what to skip. Also (everyone), sorry I overcomplicated with @adjust in pwc_px() and ugly_x, the array and adjustment itself should be omitted; it's leftover from previous approach when I tried pre-determined pattern of steps; now step is always "1" and unfriendly numbers explicitly skipped; so just start from $from. Damn ;-). I'm grateful not to have published yesterday; with a few more blunders; hopefully this "@adjust" is the only left

In reply to Re^2: Faster (but uglier) PWC 350-2 solutions by Anonymous Monk
in thread Faster (but uglier) PWC 350-2 solutions by Anonymous Monk

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