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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.

Crypto Conundrum: Newsletter Challenge (December 2016)

Posted December 01, 2016 12:00 AM
Pathfinder Tags: challenge questions

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

A security consultant wants to monitor the communications of a target who is using a system secured by an SSL/TLS connection thought to be unbreakable. The connection’s encryption keys are generated by an elliptic curve random number generator. Is it possible for the consultant to break into the target’s communications? How could he do it?

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

9 comments; last comment on 12/04/2016
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Natural Variations: Newsletter Challenge (November 2016)

Posted October 31, 2016 12:00 AM
Pathfinder Tags: challenge questions

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

Natural variations in repeated measurements form a normal distribution. Ten recent measurements are made where the average and standard deviation of the measurement is known from many previous measurements. How many times more likely is it that none of the ten recent measurements will occur outside of 2 standard deviations of the average as compared to outside of 1 standard deviation of the average?

And the answer is:

When dealing with normal distributions, the probability of a data point occurring within 1 standard deviation is 68.27%. The probability of a data point occurring within 2 standard deviations is 95.45%. The odds that 10 recent measurements all fall within 1 standard deviation is 0.6827*0.6827*0.6827*0.6827*0.6827*0.6827*0.6827*0.6827*0.6827*0.6827=0.682710=0.022=2.2%

Similarly, the odds that 10 recent measurements all fall within 2 standard deviations is (0.954510=0.6277=62.8%). Since 0.6277/0.022=28.5, it is 28.5 times more likely that ten measurements will fall within 2 standard deviations than 1 standard deviation. This makes sense since 2 standard deviations provides more room for measurement variation than 1 standard deviation.

6 comments; last comment on 11/17/2016
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The Occasional Spark: Newsletter Challenge (October 2016)

Posted October 01, 2016 12:00 AM
Pathfinder Tags: challenge questions

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

Sharp or pointed objects in the air – like a ship’s mast, an antenna – sometimes produce electric sparks at the tip of the object. What causes these sparks?

And the answer is:

These sparks, called St. Elmo’s fire or a corona, are due to the electrical breakdown of the air close to the sharp tip of a conducting object. This phenomenon happens when the electric field in the air is stronger than normal. But at the tip of the sharp object – where charges gather - it is even stronger; the field, then, can pull electrons out of air molecules and accelerate them. These electrons collide with air molecules and excite them. When these molecules eventually de-excite they produce light that can be seen.

20 comments; last comment on 10/16/2016
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Sluggish Growth: Newsletter Challenge (September 2016)

Posted September 01, 2016 12:00 AM
Pathfinder Tags: challenge questions

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

A researcher studying the velocities of various natural processes is impressed by the glacial pace of one in particular, taking place at a rate of approximately 317 am/s. Occurring at great depths on Earth, it involves the formation of materials of economic interest. What is the process?

And the answer is:

The formation of manganese nodules is one of the slowest processes on Earth, accumulating at a rate between 10 to 100 millimeters per million years. The nodules grow by the precipitation of metal compounds out of ocean water around a nucleus such as a piece of shell on the ocean floor. There are two methods by which this process commonly takes place: hydrogenous growth and diagenetic growth. Hydrogenous growth largely involves precipitation of the manganese oxide mineral vernadite that forms naturally in the ocean. Diagenetic growth is unique in that it involves ocean water that has been enriched with metal compounds gathered after reacting with sediments in the sea floor. Upon emerging from the sea floor, the metal – usually the manganese oxides todorokite and birnessite – contained in this pore water is deposited onto the growing nodules. Most manganese nodules are a mixture of the two processes.

Because of the slow timescale of their growth, manganese nodules tend to grow only in regions of relatively stable environmental conditions such as those provided by a plentiful flow of Antarctic bottom water. This flow clears out fine sediment that would otherwise cover up newly forming nodules, while also stimulating transport of oxygen rich water from the surface to the depths.

The nodules contain a variety of metals other than manganese, including iron, copper, nickel, cobalt, titanium, tellurium, thallium, zirconium, and rare earth elements. This elemental bounty has attracted the attention of mining interests in the past, although the investment required to carry out operations has so far deterred any significant mining projects.

10 comments; last comment on 09/28/2016
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Pulsar Astronomy: Newsletter Challenge (August 2016)

Posted August 01, 2016 12:00 AM
Pathfinder Tags: challenge questions

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

A double pulsar system is considered a terrific object for studying relativity. However it also can offer great insights into QED. What is it about that particular type of system, particularly the space close to that system, which makes it so useful for studying QED?

And the answer is:

In QED, a large magnetic field can cause the refractive index of space to vary with the polarization of light passing through it, effectively making the light birefringent. Light passing through such space will emerge with a slight elliptical polarization. The amount of elliptical polarization can be used to test QED theories about vacuum polarization.

http://physicsworld.com/cws/article/news/2006/mar/27/optical-rotation-sheds-light-on-vacuum

http://iopscience.iop.org/article/10.1088/0264-9381/26/7/073001

http://arxiv.org/pdf/quant-ph/0504039.pdf

13 comments; last comment on 08/23/2016
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