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+# Increment base-10 number by 1
+#
+# Copyright (C) 2018 Mike Gerwitz
+#
+#  This program is free software: you can redistribute it and/or modify
+#  it under the terms of the GNU General Public License as published by
+#  the Free Software Foundation, either version 3 of the License, or
+#  (at your option) any later version.
+#
+#  This program is distributed in the hope that it will be useful,
+#  but WITHOUT ANY WARRANTY; without even the implied warranty of
+#  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+#  GNU General Public License for more details.
+#
+#  You should have received a copy of the GNU General Public License
+#  along with this program.  If not, see <http://www.gnu.org/licenses/>.
+#
+# This shows how to perform basic arithmetic on numbers using regular
+# expressions.  The method is outlined below.  It's easy to see that, for
+# any base-N number of M digits, we need NM regexes.  For K such numbers, we
+# need NMK regexes.  The more M or K we have, the more complex the regexes
+# become to handle the offsets.  (The use of the `^' and `$' anchors alone
+# for replacements are only sufficient for M≤3 when K=1; what do we have to
+# do when M>3 to replace only the digits we are interested in?)
+#
+# It is possible to subtract using the same concept.  Further, since we can
+# implement addition and subtraction, we can also implement multiplication
+# and division.
+#
+# TO USE: Provide a 0-padded 3-digit base-10 number.  Each time this script
+# is run, the number will be incremented by one.  Exits with exit code 1 if
+# a non-3-digit-number is provided; and 2 once we cannot count any higher.
+##
+
+# Input must only be numbers
+/^[0-9]\{3\}$/!q1
+
+# Increment 1s (third character).  If we overflow, represent the overflow as
+# an `A', which is then handled below.
+s/9$/A/
+s/8$/9/
+s/7$/8/
+s/6$/7/
+s/5$/6/
+s/4$/5/
+s/3$/4/
+s/2$/3/
+s/1$/2/
+s/0$/1/
+
+# Carry 10s by converting the overflow character `A' to a `0' and
+# incrementing the 10s position.
+s/9A$/A0/
+s/8A$/90/
+s/7A$/80/
+s/6A$/70/
+s/5A$/60/
+s/4A$/50/
+s/3A$/40/
+s/2A$/30/
+s/1A$/20/
+s/0A$/10/
+
+# Same as above, but for 100s.
+s/^9A/A0/
+s/^8A/90/
+s/^7A/80/
+s/^6A/70/
+s/^5A/60/
+s/^4A/50/
+s/^3A/40/
+s/^2A/30/
+s/^1A/20/
+s/^0A/10/
+
+# Any remaining carry flags means we can't count any higher.
+/A/!b; q2