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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.

Birthday Trio: Newsletter Challenge (April 2014)

Posted March 31, 2014 5:01 PM
Pathfinder Tags: challenge questions

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

A school teacher notices that 3 students in his class of 30 students share the same birthday. What is the percent chance of this occurring?

Assume all days of the year are equally likely as a birthday, ignore leap years, and assume the class represents a random sample of birthdays.

The answer to this question will appear later this month, right here on CR4.

84 comments; last comment on 04/19/2014
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Is Diet Soda Really Light?: Newsletter Challenge (March 2014)

Posted March 01, 2014 8:00 AM
Pathfinder Tags: challenge questions

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

A can of a diet refreshment (such as a Diet Coke) and a can of regular refreshment (such as a regular Coke) are placed inside a bucket of water. Both cans contain exactly the same volume of liquid and the cans are identical in size and shape. Which can will float higher relative to the other?

And the answer is:

Sweetening regular soft drinks requires large amounts of sugar. The sugar will be dissolved in the liquid with only a small increase in volume. Remember also that the density of sugar water is greater than that of regular water. Diet drinks require artificial sweeteners to sweeten the drink, but a very small amount of the artificial sweetener will suffice. So the diet drink density is slightly heavier than regular water. Therefore the regular Coke will sink, or will at least float lower than the diet drink.

38 comments; last comment on 03/26/2014
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Icy Explanation: Newsletter Challenge (February 2014)

Posted February 01, 2014 12:00 AM

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

Isabella is living in an outpost on the surface of a super-Earth-sized exoplanet. The air temperature has been a constant -7.6°F (-22°C) for a month. Outside sits a glass of water. Occasionally a thin layer of ice can be seen at the bottom of the glass, other times the ice is floating on top, and sometimes there is no ice at all. What is causing this?

And the answer is:

The atmospheric pressure of the exoplanet at the habitat must be around 209.9 MPa (2071 atm). Ice has a triple point between ice Ih (regular ice), ice III, and water at a temperature of 251.165 K and a pressure of 209.9 MPa. Ice Ih is less dense than water, whereas ice III is denser than water. Small fluctuations in the atmospheric pressure at the habitat are causing the changes. The pressure fluctuations must be transient since only a small layer forms.

24 comments; last comment on 02/26/2014
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Brass Plate Heating: Newsletter Challenge (January 2014)

Posted January 01, 2014 12:00 AM

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

A brass plate with a hole in the middle is heated from room temperature to 60°C.

Does the hole get bigger, smaller, or remain the same size?

And the answer is:

The hole will become bigger. In linear thermal expansion the distance between two points on the brass plate increases proportional to the increase in temperature. The distance between two corners, for instance, will increase, as well as the diameter of the circle. The expansion inward into the hole will make the diameter smaller, contradicting the principle of linear thermal expansion. Some readers may say that there will be an expansion of the distance in the figure. This is correct, but the expansion does not take place by pushing point d toward the center of the hole, but because there is an expansion of the distance

41 comments; last comment on 01/21/2014
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Expansive Expansion: Newsletter Challenge (December 2013)

Posted December 01, 2013 12:00 AM
Pathfinder Tags: challenge questions

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

A binomial raised to the 3rd power and then algebraically expanded has binomial coefficients of 1, 3, 3, 1. What are the binomial coefficients when a binomial is raised to the 16th power?



And the answer is:

Pascal's Triangle makes this an easy problem to solve. Simply use the bottom row below to obtain the coefficients for each term. For trinomial expansions there is a similar tool called Pascal's pyramid.

15 comments; last comment on 12/04/2013
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Spark Safety: Newsletter Challenge (November 2013)

Posted October 31, 2013 5:01 PM

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

If you work at a mine, a flour mill, or a similar environment, you must take extraordinary precaution not to produce any electrostatic spark. Why is this important and required by law?

And the answer is:

In these types of environments there is airborne powder. Powder particles in bulk, for example inside a bag, do not burn when subjected to a spark because all the particles or grains are surrounded by other grains. When the power is airborne the particles are surrounded by air. When a spark occurs this air provides enough oxygen to start the burning process very quickly. Once burning starts at any point in the dust, the thermal energy is transferred very rapidly from particle to particle, producing an explosion.

52 comments; last comment on 12/13/2013
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