There's the 20-questions game of: client trying to guess a server-chosen integer. The server responds with one of higher, lower or yes to any guess from the client. The best strategy for such a game is to always guess halfway between the current possible range. This is because you are essentially doing a binary search and want to eliminate the biggest possible range with your every question, slowly zooming-in to the correct answer.

The output of a hashing algorithm can be labelled as a unique non-negative integer (or be converted to one). SHA1 has 160 bits of output. Giving the possible guesses to be in the range 0 to 2^160 = 0 to 1461501637330902918203684832716283019655932542976. The best guess would be 2^160/2. If the server answers with try lower, then your next guess should be 2^160/4.

Bonus points for how many guesses guessing a SHA1 hash needs, given that the server is ever so helpful in giving us 2 bits of information each time. But from what I gather from this post's little 20-questions game, the server does give hints (e.g. Then the server answers yes/no, or gives some hint.)

Here is something to play with, if indeed your problem falls in this category (it certainly did keep me entertained for a while):

# by bliako on 30/08/2021
# for https://perlmonks.org/?node_id=11136212

use bigint qw/hex/;
use Digest::SHA1 qw/sha1 sha1_hex/;

my $digest_hex = sha1_hex('blah blah blah');
my $answer = hex($digest_hex);
print "$0 : starting with this number: $answer.\n";

my $min = 0;
my $max = 2**160;

my $num_guesses = 0;
my ($guess, $diff);
while( ++$num_guesses ){
    $guess = $min + ($max - $min) / 2.0;
    $diff = $guess - $answer;
    print "entering at guess number $num_guesses, current range:\n  mi
+n: $min\n  max: $max\n  answer: $answer\n  guess: $guess\n  diff: $di
+ff\n";

    if( $guess < $answer ){
        print "your guess ($guess) needs to go higher ...\n";
        $min = int($guess);
    } elsif( $guess > $answer ){
        print "your guess ($guess) needs to go lower ...\n";
        $max = int($guess);
    } else {
        print "bingo in $num_guesses guesses! the answer was: $digest_
+hex and your guess was ".bigint_to_hex($guess)." ($guess).\n";
        last;
    }
}

sub bigint_to_hex {
        # graduitously ripped off from Ben Aveling's answer in
        # https://stackoverflow.com/questions/828462/how-can-i-sprintf
+-a-big-number-in-perl
        # because sprintf("%x", bigint) does not work sadly...
    my $inp = shift;
    my $out = "";
    while($inp){
        my $chunk=$inp & 0xf;
        $inp >>= 4;
        $out = sprintf("%x",$chunk).$out;
    }
    return $out;
}
[download]

entering at guess number XXX, current range:
  min: 216530321997656745029789011476757518019484653536
  max: 216530321997656745029789011476757518019484653568
  answer: 216530321997656745029789011476757518019484653552
  guess: 216530321997656745029789011476757518019484653552
  diff: 0
bingo in XXX guesses! the answer was: 25ed8e31b995bb927966616df2a42b97
+9a2717f0 and your guess was 25ed8e31b995bb927966616df2a42b979a2717f0 
+(216530321997656745029789011476757518019484653552).
[download]

EDIT: this is interesting reading

bw, bliako