I considered do {} while, but that required declaring the variables outside the loop and, besides, I felt there was some virtue in showing OP the bare block trick.

Using the comma operator:

use strict;
use warnings;

1 while (print "Guess the Code: "), <> != (1+int rand 10);
print "\n  Time taken to break the Code ..: ", time()-$^T, " seconds\n
+";
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gets the prompt printed for each iteration.

Using $^T is nice btw. Something I'd not have thought of - I'm still learning. :)