Ring of Bits
Brain Warm-up	Simplified Math 423 Homework problem

Problem:

Puzzle 1: There are eight unique 3-digit binary numbers (000, 001, 010, 011, 100, 101, 110, & 111). You can draw a circle of ones and zeros it such a way that each of these 8 combinations can be found by picking the correct starting place on the circle and reading the digits clockwise. For example, in the picture shown here, “101” can be found boxed in green and “011” can be found boxed in blue. Drawing this circle would be easy if it contained 24 binary digits because you would not have to make any of the eight sequences overlap. Your job, however, is to make a circle using only eight digits. Obviously, in this circle every digit will be the start of a unique sequence of three. Bonus: Do the same thing with 4-digit binary numbers and a 16-digit circle.

Solvers:

Mike Grim (solved: 6:33pm 2-21-2005) tom von kercey (solved: 8:31pm 2-21-2005) eeyalpud ydna (solved: 9:51pm 2-21-2005) dan (solved: 12:33am 2-22-2005) John Tippabattuni (solved: 9:40am 2-22-2005) Erin (solved: 11:48am 2-22-2005) Josh Giedeman (solved: 8:14pm 2-23-2005) Jonathan (solved: 9:10pm 2-23-2005) bill (solved: 11:48am 2-24-2005) the greathoj (solved: 3:32am 2-28-2005) = Solved the problem and the bonus.

Solution:

There are many solutions for both the problem and the bonus. To find a solution start at any node in the graph (below) and traverse the graph by following the directed edges without visiting a node twice.

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