Here are some math and logic puzzlers re-written for the Star Trek crowd. While I grew up with classic Trek, and Spock remains my favorite Trek character, I must grudgingly admit that the old series looks pretty creaky and amateurish these days. Sigh. So I've written these questions based around the Next Generation/Deep Space 9 era. Since I am no math genius, I have enlisted the aid of Robert Carvalho, Star Trek expert and puzzle whiz. Rob helped me edit and check the quiz answers.
Answers and winner are here.
1. A popular holodeck target practice game has opponents shooting lights as they move and change color. Guinan whipped Worf's butt in one game in the episode "Redemption". (Aside: Why is it that Klingons can only beat other Klingons?) To soothe his wounded pride, Worf arranges a shipwide tournament, in which 637 people (including crewmembers and guests) enter. If competitors face each other in pairs, with the loser automatically and irrevocably eliminated (receiving no consolation prize, but only shame on his/her family name for three generations), how many matches must be played to determine a winner?
2. In the episode "Relics," the starship Enterprise discovers an alien Dyson sphere. This is an enormous ball (millions of kilometers in diameter) which is centered around and captures energy from a star. While examining the Dyson sphere, a young Geordi La Forge and an aged Montgomery Scott discover that there are two communications lines that completely encircle the sphere. The lines are parallel to and 3 kilometers north of the equator of the sphere. One line is on the outside of the sphere, while the other is directly opposite on the inside; the Dyson sphere is three meters thick. The Enterprise becomes trapped inside the sphere, and Scotty suggests a plan to get it out. But LaForge thinks the plan is hair-brained and fears the old geezer has gone batty. To test him, Geordi asks, "How much longer is the outside line than the inside one?" Scotty, apparently still in complete command of his faculties, readily answers. He thus regains Geordi's trust and together they free the Enterprise from the sphere. What was Mr. Scott's answer?
3. Riker and an away team beam down to the planet Pognarinor. The inhabitants (Pognari) conveniently speak English, using familiar verbs, adjectives and nouns, but their units of measurement are unusual. They measure distances in "fignets." The Pognari are an advanced and orderly race. They decided on a particular length for a standard fignet because the planet's surface area in square fignets is exactly equal to its volume in cubic fignets. The Enterprise's scanners have determined that Pognarinor is 24,000 km in diameter. Assuming that the planet is perfectly spherical, how many km is a fignet?
4. Counselor Deanna Troi's annoying and meddling mother, Lwaxana, is on her way to Starbase 17 and has hitched a ride aboard the Enterprise. The ship is bound for asteroid N4G7, where it will rendezvous with a shuttlecraft from the starbase, which will bring Lwaxana directly to the starbase. The Enterprise arrives at the asteroid an hour early. However, Captain Picard has found Lwaxana to be such an intolerable nuisance that he starts the ship immediately toward the starbase, at a constant speed of quarter impulse (0.25 times the speed of light). The shuttlecraft meets the Enterprise en route, and Lwaxana is instantly and unceremoniously transported aboard. Picard breathes a big sigh of relief. The shuttlcraft arrives at Starbase 17 ten minutes earlier than planned. Assuming that the shuttle traveled at a constant speed and that it left the starbase just in time to arrive at N4G7 at the scheduled hour, how much earlier than planned did Picard get rid of Lwaxana?
5. The android Data pilots a shuttlecraft down to a planet of storms. His mission: to rescue the survivors of a crashed scoutship carrying human and Vulcan scientists. Because of high levels of Piranesi radiation, neither the ship's sensors nor Data's hand-held instruments can determine exactly how many survivors there are. On the planet's surface, Data meets a Vulcan woman. She is fascinated by Data's workmanship and wants to test his abilities. When Data asks her the number of survivors, the Vulcan states coyly, "If you come upon any two survivors, there is - in human terms - an even-money bet that both will be Vulcans." Knowing that the scoutship could carry, at most, 14 total, Data smiles and announces the number of survivors. The Vulcan congratulates him, calls for her friends, and together they leave the planet. How many survivors were there?
6. A new subatomic particle called the "bozon" has been discovered and is being tested for use in high-speed communication. The Enterprise and various other ships are involved in precision flying exercises in wargames. The frigate Addison is following the Enterprise at a constant distance of exactly 50 km while both are traveling at warp nine. To avoid collisions, computers aboard the ships are in constant communication, sending back and forth packets of bozons, which contain data on each ship's velocity, position and direction. The Addison's computer sends a query about velocity to the Enterprise, which then responds. In the total time it takes the query bozons to travel from Addison to Enterprise and reply bozons to travel from Enterprise to Addison, the ships have traveled 50 km. Assuming that the bozons traveled at constant speed and that the Enterprise answered the query instanteously, how many km total did the query and reply bozons travel?
7. If there are more Klingons on a ship than there are forehead wrinkles on any one Klingon, must there be two Klingons with the same number of cranial krinkles? Assume each Klingon has at least one krinkle.
8. Captain Benjamin Sisko has a son, Jake, and a father, Joseph. When Benjamin is as old as his father is now, he shall be five times as old as Jake is now. By then, Jake will be 8 years older than Benjamin is now. The combined ages of Ben and Joseph is 100. How old is Jake?
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