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Honors Algebra Two - Goal Sequence











































starting from an initial sequence of * and @ get to the goal sequence in a certain number of moves. To do this you can use 3 replacement rules, one at a time, on a consecutive substring of the present sequence. You never need more than 6 symbols. Below is a sample puzzle and its solution.

Rule 1: @ → *@
Rule 2: *** → @@
Rule 3: @* → @

Goal: *@@ → @**@@@ in 5 moves
*@@ → **@@ → ***@@ → @@@@ → @*@@@ → @**@@@

My problem:

Rule 1: @@ → **@
Rule 2: @*→ @@@
Rule 3: **@ →**

Goal: @* → **@*** in 12 moves

Comments for Honors Algebra Two - Goal Sequence

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Oct 06, 2011
Replacement Puzzle
by: Staff


Question:

starting from an initial sequence of * and @ get to the goal sequence in a certain number of moves. To do this you can use 3 replacement rules, one at a time, on a consecutive substring of the present sequence. You never need more than 6 symbols. Below is a sample puzzle and its solution.


Rule 1: @ → *@
Rule 2: *** → @@
Rule 3: @* → @

Goal: *@@ → @**@@@ in 5 moves





My problem:

Rule 1: @@ → **@
Rule 2: @*→ @@@
Rule 3: **@ →**

Goal: @* → **@*** in 12 moves




Answer:


Rule 1: @@ → **@
Rule 2: @*→ @@@
Rule 3: **@ →**

Goal: @* → **@*** in 12 moves


I’m going to refer you to a master of replacement puzzles: Erich Friedman, Associate Professor of Mathematics and ex-Chair of the Math and Computer Science Department at Stetson University.

His excellent website shows step by step solutions to 58 different replacement puzzles.


(1) If your browser is Firefox, click the following link; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www2.stetson.edu/~efriedma/replace/



Thanks for writing.

Staff
www.solving-math-problems.com



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