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  • \$\begingroup\$ This is, of course, much faster, but it doesn't fulfill the question's requirements. key can be any integer, not digit, between lo and hi. \$\endgroup\$ Commented Feb 11, 2014 at 17:31
  • \$\begingroup\$ there is still a mathematical solution, though it would be even longer... \$\endgroup\$ Commented Feb 11, 2014 at 22:46