Texas College Mathematics Journal
Vol. 2 (2005), pp. 1-9.

Subtractive Black Holes and Black Loops

MURRAY H. SIEGEL, WASIN SO AND PETER A. COOPER

MSC (2000): Primary 97 - 02

Key words: Subtractive process, Kaprekar constant, unique terminations

Abstract: Subtractive black holes and black loops are generalizations of Kaprekar's constants. When the subtractive Kaprekar routine is applied to an n-digit number a termination in the form of a black hole or black loop is reached. If all n-digit numbers for a specific value of n, other than numbers where all digits are the same, result in the same black hole then that number is a Kaprekar constant. The process and its results provide a rich environment for conjecture and proof.

Mathematics & Computer Science Division, South Carolina Governor's School for Science & Mathematics, SC

E-mail address: siegel@gssm.k12.sc.us

Received by Editor: April 18, 2004 and, in revised form August 3, 2005.
Posted: August 17, 2005.

Copyright 2005