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Challenge Questions

Stop in and exercise your brain. Talk about this month's Challenge from Specs & Techs or similar puzzles.

So do you have a Challenge Question that could stump the community? Then submit the question with the "correct" answer and we'll post it. If it's really good, we may even roll it up to Specs & Techs. You'll be famous!

Answers to Challenge Questions appear by the last Tuesday of the month.

100 Meter Dash: Newsletter Challenge (April 2015)

Posted April 01, 2015 12:00 AM
Pathfinder Tags: challenge question

This month's Challenge Question: Specs & Techs from IHS Engineering360:

Now that good weather is around the corner, a challenge question related to outdoor activities is a must. In short races (100 meters or less) breathing is not necessary for the runner. Why?

The answer to this challenge will be posted later this month, right here on CR4.

3 comments; last comment on 04/01/2015
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3464-Cube: Newsletter Challenge (March 2015)

Posted February 28, 2015 5:01 PM

This month's Challenge Question: Specs & Techs from IHS Engineering360:

A 2-cube (square) has 4 vertices and 4 edges. A 3-cube (cube) has 8 vertices, 12 edges, and 6 faces. A 4-cube (tesseract) has 16 vertices, 32 edges, 24 faces, and 8 cells. In three dimensions, the Euler characteristic says that vertices + faces - edges = 2. What is the right side of the Euler characteristic equation equal to when generalized and calculated for a 3464-cube?

And the answer is:

The answer is 0. The vertex (0-face), edge (1-face), face (2-face), cell (3-face), 4-face, etc. are the smaller dimensional objects that make up a larger dimensional shape. There are always n-1 dimensional objects that make up an n dimensional shape.

For instance, in 2 dimensions, a square is made up of 1 dimensional lines (edges) and the zero dimensional points (vertices). A three dimensional cube is made up of 2 dimensional sides (faces), 1 dimensional lines (edges) and zero dimensional points (vertices). When the Euler Characteristic is generalized for all dimensions, it says add up the number of even dimensional components and subtract from them the number of odd dimensional components. For an n-cube, that difference will be 0 if n is even and 2 if n is odd. So in the case of a cube in three dimensions, vertices + faces - edges = 2. For a 3464-cube, vertices + faces + 4-faces +…+ 3462-faces - edges -cells - 5-faces - … - 3463-faces = 0.

http://en.wikipedia.org/wiki/Hypercube#Elements (See Hypercube Elements Chart)

Editor's Note: This question was previously titled "3463-Cube." It was an error and has since been corrected to "3464-Cube."

21 comments; last comment on 03/17/2015
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Jovian System: Newsletter Challenge (February 2015)

Posted February 01, 2015 12:00 AM
Pathfinder Tags: challenge question

This month's Challenge Question: Specs & Techs from IHS Engineering360:

It's 2045 and a group of space pioneers are on an interplanetary transport to the Callisto colony. The pioneers were awoken from a four-year hibernation, having traveled to Jupiter's orbit only to find a large dumbbell-shaped asteroid several hundred kilometers wide where they expected Jupiter to be. Where are they?

And the answer is:

The transport must have had a critical navigation error early in the trip because it sounds like they have reached Jupiter's leading Lagrangian point, L4 , and are viewing 624 Hektor, the largest of Jupiter's Trojans.

"624Hektor-LB1-mag15" by I, Kevin Heider. Licensed under CC BY-SA 3.0 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:624Hektor-LB1-mag15.jpg#mediaviewer/File:624Hektor-LB1-mag15.jpg

39 comments; last comment on 02/18/2015
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Launch Location: Newsletter Challenge (January 2015)

Posted January 01, 2015 12:00 AM
Pathfinder Tags: challenge question

This month's Challenge Question: Specs & Techs from IHS Engineering360:

The Kennedy Space Center at Cape Canaveral is located at latitude 28.5° North. Besides being close to the Equator to facilitate launching, why is this latitude especially important for launching lunar satellites? The center's location gave clear edge to the US Apollo program compared to the Soviet satellite launch location at Tyuratam.

And the answer is:

The orbit of the Moon is affected by the gravity exerted by the Sun, causing the lunar orbit to be inclined by about ±5 degrees and 9 minutes with respect to the Earth's orbital plane. Add this to the normal tilt of the Earth's Equator with respect to the orbital plane 23 degrees and 28 minutes, the inclination of the Moon orbit with respect to the Earth's Equator varies from 18 degrees and 19 minutes to 28 degrees and 37 minutes, close to the exact latitude of Cape Canaveral. This allowed NASA to launch the spacecraft directly into orbits that lie almost exactly in the plane of the moon.

On the other hand, the Soviet launch site is located at 45.6 degrees North latitude. They had to launch the spacecraft into an orbit with inclination of 45.6 degrees; this orbit is inclined about 17 degrees respect to the lunar orbit. Once the spacecraft is in this plane, it must change direction to the Moon's orbital plane, requiring high fuel consumption and complicated logistics.

11 comments; last comment on 01/13/2015
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Autumnal Glow: Newsletter Challenge (December 2014)

Posted December 01, 2014 12:00 AM
Pathfinder Tags: challenge question

This month's Challenge Question: Specs & Techs from IHS Engineering360:

It is a new moon and Lee is taking a predawn stroll on a beach on the east side of Nantucket admiring the stars. As he looks out over the Atlantic Ocean, he notices what seems to be the soft glow of light pollution from a city off in the distance. What is Lee seeing?

And the answer is:

Lee is seeing the zodiacal light, a faint, conical, diffuse white glow seen along the elliptic near the horizon. It's caused by sunlight scattered by the interplanetary dust cloud of our solar system.

63 comments; last comment on 12/21/2014
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Icy Imbalance: Newsletter Challenge (November 2014)

Posted November 01, 2014 12:00 AM
Pathfinder Tags: challenge questions

This month's Challenge Question: Specs & Techs from IHS Engineering360:

The two poles of the Earth contain ice. Why does Antarctica have much more ice (about ten times more) than the Arctic?

And the answer is:

Ice in the arctic circle is over the ocean, while Antarctica is a solid landmass. Water has a high heat capacity, so it takes a long time to absorb heat, but also a long time to lose heat. During summer the Arctic water stores heat and in winter it releases it. On the other hand, land does not have a high heat capacity so it releases heat very fast, keeping the land to a lower temperature all year round.

20 comments; last comment on 11/26/2014
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