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Can You Find Spock By Solving This 1983 Math Problem?

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Published in the May 1983 issue of the journal Mathematics Teacher, this amazing math problem challenges students to locate the USS Enterprise's missing first officer—in 50 minutes or less—using compass and straightedge. Are you up to the task, cadet?

This is a compass-and-straightedge construction math problem, so you'll need to put down your laptop and do this old school. The map of the Star Trek galaxy—complete with the Romulan Neutral Zone and Tholian Web—is reproduced below, followed by the original step-by-step instructions.


Now, go find Spock.



These are the voyages of the starship Enterprise. Its five-year mission—to explore strange new worlds, to seek out new life and new civilizations, to boldly go where no man has gone before. Wait a minute ... Where's Spock? Spock? Spock ? We've got to find Spock!

Your assignment, as Captain of this starship, is to help the crew of the Enterprise find its first officer, Spock. To do this, you must find ten new points on the accompanying chart. To find these points, follow in order the directions given. You have only fifty minutes before your command is revoked and you are reassigned to menial work. In following the directions, use the circled dots that are part of each object pictured. The Romulan neutral zone should be considered as a line.

l. Warp out oforbit to find point 1 midway between the Klingon ship and Earth.

2. To find point 2, proceed three-fourths of the distance from point 1 to Apollo's hand. (The point on Apollo's hand is on the watchband.)


3. To find point 3, change course by 45° in a counterclockwise direction, heading toward the Romulan neutral zone until you intersect the line that bisects the angle formed by the planet killer, the Tribble asteroid, and the Jupiter 2.

4. Take an immediate course change heading directly for the nova from point 3. You will find point 4 at a distance equal to three times the distance between the edge of the galaxy and the Enterprise.


5. The nova's heat drives your crew berserk, and they lose control of the ship. You find yourself at point 5 when you regain control. Point 5 is an equal distance from point 4, the time portal, and the planet killer.

6. From point 5, under sealed orders, proceed to point 6, which is at the edge of the Romulan neutral zone. Be sure to take the shortest route. (To keep your worksheet from getting too cluttered, you may want to move point 6 to a clean copy of the sheet.)


7. After accomplishing your mission at the edge of the Romulan neutral zone, return toward the Enterprise. To avoid a space radiation belt, you stop at point 7, which is one-third ofthe distance between point 6 and the Enterprise.

8. Starfleet Command instructs you to proceed to point 8 along a line that is parallel to the line between the time portal and the asteroid belt. You find point 8 on this line at a distance equal to the distance between point 7 and the Tribble asteroid.


9. Meteor shower! You veer off course to find point 9. It is where the perpendicular line from point 8 intersects the line between the Klingon ship and the planet killer.

10. You find Spock at point 10, which is equidistant from the three lines that connect point 9, the Tholian web, and the asteroid belt.


CONGRATULATIONS to those of you who found Spock! You will proceed to advanced mathematics where you will pick up your commissions. The rest of you... get your brooms and get to work.