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### Comment on

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Not a golfing solution, but one that doesn't assume an upper bound (although it will loop forever if there's no finite answer):
```use strict;
use warnings;
use Test::More 'no_plan';

\$| = 1;

my %cache;

sub exact {
my (\$amount, @bills) = @_;
return \$cache{\$amount} if defined \$cache{\$amount};
return 1 if !\$amount;
return 0 if  \$amount < 0;
foreach my \$bill (@bills) {
return \$cache{\$amount} = 1 if exact(\$amount - \$bill, @bills)
}
return \$cache{\$amount} = 0;
}

sub largest {
%cache = ();
my @bills    = @_;
my \$smallest = \$bills [0];
return -1 if \$smallest == 1;
my \$start = 0;
my \$prev  = 0;
for (my \$t = 1; 1; \$t++) {
if (exact(\$t, @bills)) {
if (\$prev) {
if (\$t - \$start + 1 == \$smallest) {return \$start - 1}
}
else {\$start = \$t}
\$prev = 1;
}
else {
\$prev = 0;
}
}
}

is (largest(6,9,20),                            43);
is (largest(3,5),                                7);
is (largest(6,11,20),                           27);
is (largest(17,18,19,20),                      101);
is (largest(2,3,5,10),                           1);
is (largest(1000,1001,1002,1003,1004,1005), 199999);

__END__
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In reply to Re: Golf: Buying with exact change by Anonymous Monk

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