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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.

Satellite Struggle: Newsletter Challenge (June 2017)

Posted May 31, 2017 5:01 PM
Pathfinder Tags: challenge question satellite

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

Column 54 through 61 of a TLE set for the IRIDIUM 20 satellite has a value of -21027-4. What is this number’s meaning, and what are the physical implications of its negative value?

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

3 comments; last comment on 05/31/2017
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Frustrating Fastballs: Newsletter Challenge (May 2017)

Posted April 30, 2017 5:01 PM
Pathfinder Tags: baseball challenge question

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

Once in a while you may hear a baseball player describe a pitcher’s pitch as a “rising fastball.” This seems to violate the laws of physics because a baseball is subject to gravity and should immediately have a downward acceleration, in addition to its forward acceleration, when released by a pitcher. Thus a pitch that rises should be impossible. What’s going on?

And the answer is:

Batters divide a pitch into thirds. During the first third the batter is picking up the ball after the pitcher releases it. The second third has the batter anticipating the timing and location of the swing needed to hit the ball. Finally the third part is the batter swinging the bat. So when a pitcher throws several 90-mph fastballs in a row, the batter develops a mental model for the trajectory of that pitch. Baseball announcers will often call this “getting the pitcher’s timing down.”

Some pitchers will occasionally throw a faster version of their fastball to throw off the batter’s timing. For example, that pitcher throwing 90-mph might slip in a 95-mph fastball one pitch. The batter picks up the ball but doesn’t notice the 5 mph difference in speed. The batter calculates where the 90-mph fastball would go and swings at that spot. But the 95-mph fastball has a flatter trajectory. It doesn't drop quite as much from the pitcher to plate because it's going faster.

This results in the batter swinging under the pitch. The pitch appears to be higher than the batter expects and to the batter the pitch seems to “rise”. Thus the rising action sometimes described by hitters is actually a result of mental miscalculation. Crafty veteran pitchers will sometimes exploit this effect by subtly varying their pitch speeds by using modified grips.

https://uanews.arizona.edu/story/the-myth-of-the-rising-fastball-and-searching-for-the-ideal-baseball-bat

27 comments; last comment on 06/02/2017
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Baffling Beer Glasses: Newsletter Challenge (April 2017)

Posted March 31, 2017 5:01 PM
Pathfinder Tags: beer challenge question optics

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

Typical beer mugs have thick walls and a thick bottom. This design serves two purposes. First, it makes the mug heavier, so the drinker assumes the beer is “good.” The second reason is to give the impression that the mug holds more beer than it actually does. Why is this so? Why would the volume appear greater than it is?

And the answer is:

This is an illusion caused by refracted light coming from the beer and passing through the glass and then moving into the air. See, for example, the following figure in which a ray leaves the left edge of the beer. When the ray reaches the edge of the mug it bends when it reaches the air near a viewer’s eyes.

When the viewer’s eyes interact with the ray they mentally extend it back into the glass (mug) and conclude that the original start of the ray is to the left of the actual starting point, as shown in the figure. The mug appears to have a bigger diameter, so the drinker assumes they will enjoy more beer than they actually paid for. Of course, the bartender is happy!

27 comments; last comment on 04/25/2017
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Answer: Prime Partition, March 2017 Challenge Question

Posted March 30, 2017 5:46 PM

Question:

If p(n) is the number of partitions of n, defined as the number of ways to write the integer n as a sum of positive integers where the order of the addends is not significant, what n produces the 42nd largest prime p(n)?

Answer:

The 42nd largest prime p(n) is 3513035269942590955686749126214187667970579050845937, which is produced by n = 2508.

The number of partitions p(n), as stated in the question, is defined as the number of ways to write the integer n as a sum of positive integers where the order of the addends is not significant. So, for example, for n = 4, p(4) = 5 as illustrated below:

4

3 + 1

2 + 2

2 + 1 + 1

1 + 1 + 1 + 1

A prime number is a positive integer that has no positive divisors other than 1 and itself. p(n) is prime for certain values of n, the first few of which are 2, 3, 4, 5, 6, 13, 36, 77, 111… corresponding to p(n) equal to 2, 3, 5, 7, 11, 101, 17977, 10619863,...

You can follow the latest top 20 list of largest p(n) primes at http://primes.utm.edu/top20/page.php?id=54.

8 comments; last comment on 04/03/2017
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Puzzling Prime Partition: Newsletter Challenge (March 2017)

Posted February 28, 2017 5:01 PM

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

If p(n) is the number of partitions of n, defined as the number of ways to write the integer n as a sum of positive integers where the order of the addends is not significant, what n produces the 42nd largest prime p(n)?

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

27 comments; last comment on 04/06/2017
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