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Noggin Hoggin' Challenge Starting on Monday April 15, 2013

Here are the past questions which were used in this Noggin Hoggin' Challenge, along with the answers we accepted and an explanation.

 

Bonus Question (Head Start Clue)

Perry Rover is a vegan that lives in Medicine Hat where he oversees drilling for natural gas. One sunny afternoon, he decides to go for a drive and heads east out of town on the Trans-Canada Highway. He then turns to follow Buffalo Trail south and drives a further 78.5 km before pulling over to take in the view.

Perry loves his line of work and starts imagining what would happen if we could drill right to the centre of the Earth. Then he asks himself, "Why stop there?"; what if he could drill straight through from the exact point where he stands, through the centre of the planet, to the opposite point on the other side?

Assuming he found a way to do this, what is the Binomial name of the notable native food source on the "flip-side" that could reliably satisfy his dietary restrictions, while simultaneously protecting him from certain illness?
(Do not italicize your answer)

Acceptable answers:
Pringlea antiscorbutica

Explanation:

Following Perry's road trip takes us approximately to 49° 18' N and 110° 15' W.

So, the diametrically opposite point, or antipode, on the globe is 49° 18' S and 69° 45' E.

 

Here's a breakdown of the logic:

Geographical coordinates can be measured in degrees, minutes, and seconds, the same as how time is measured in hours, minutes, and seconds. It's easier to work in decimal degrees just as how in dealing with differences in time, it can be easier to work in decimal hours, and the logic for finding the antipode makes more sense. If you worked out the starting longitudinal point to 110° 15' W, then you can convert it to 110.25 ° W (because = 0.25). However, you may even have determined the starting point at 110.25 ° W directly - resources such as Google Maps can just as easily tell you this as they can the coordinates in degrees, minutes, and seconds.

So, if the starting point has a latitude of A and a longitude of B, then the antipode simply has a latitude of -A and a longitude of B+180°.

By convention, latitude is negative in the southern hemisphere, and longitude is negative in the western hemisphere (just like in the Cartesian coordinate system). Since longitude wraps around the Earth, if the answer is outside the range of -180° to +180°, you just have to add or subtract 360° to the answer to bring it back into that range.

That brings the latitude of the antipode to -49.3 and the longitude to +69.75. Or, if you prefer the numbers to be back in DMS (Degrees-Minutes-Seconds) format, -49°, (0.3 × 60 =) 18' latitude, and 69°, (0.75 × 60 =) 45' longitude.

Of course, there are a number of websites that will do the above work for you and automatically find the antipode of any given point on Earth. Regardless of which method you used, however, you should have found yourself somewhere in the Kerguelen Islands (part of the French Southern and Antarctic Lands), more precisely on (La) Grande Terre. It is interesting to note that less than 4% of all land is actually antipodal to land, with all the rest falling somewhere in the ocean.

Since Perry Rover is a vegan, which means that he doesn't eat any meat or animal products, he would need to find a nourishing plant-based food to eat. The indigenous, Kerguelen cabbage conveniently fits the bill. It is not only edible, but also very nutritious and particularly high in vitamin C. In fact, it was historically prized for this property by passing sailors and whalers who often suffered from scurvy — a vitamin C deficiency disease. The binomial name, Pringlea antiscorbutica underlines this attribute, since "antiscorbutica" means "against scurvy" in latin.

Unfortunately, the native plant is threatened due to human activity, specifically, the inadvertent, and deliberate, introduction of invasive plant and animal species. A great article about the Kerguelen cabbage can be found at: http://www.geneticjungle.com/2009/05/kerguelen-cabbage.html

 

Kerguelen cabbage:

Mmm... looks tasty!


 

Question for Monday April 15, 2013:

Canadian Cartoon Craze

The picture montage depicts leading characters from seven popular children's television programs aired in Canada in the 1980s.

Fill in the blanks with the name of the main rival from each show. Note that each show (or a special version of it) was also produced (although not necessarily exclusively) in Canada.

Next, unscramble the circled letters to reveal the name of an eighth Canadian cartoon from the same decade.

8. _ _ _ _ _ _ _ _ _       _ _ _ _ _ _

Name the villain's sidekick from this last TV show.

Acceptable answers:
M.A.D. Cat
Mad Cat
M.A.D Cat

Explanation:

The seven television programs, along with their respective rivals, are listed below.

1. My Pet Monster – Beastur

2. The Raccoons – Cyril Sneer

3. Fraggle Rock – Gorgs

4. Strawberry Shortcake – Peculiar Purple Pieman

5. Care Bears – No Heart

6. The Adventures of Teddy Ruxpin – Quellor

7. The Get Along Gang – Catchum Crocodile

The letters appearing in the circles are e,r,s,g,g,i,p,a,n,t,e,o,c,t, and d. When unscrambled, they give us our eighth television show, Inspector Gadget.

Gadget's nemesis is the faceless Doctor Claw, and the name of his sidekick is M.A.D. Cat.


 

Question for Tuesday April 16, 2013:

I am complementary to the average of #FACE8D and #BADF00. But how much more blue light is in #C0FFEE?

(Round your answer to the nearest whole percent.)

Acceptable answers:
8
7
8%
7%

Explanation:

The codes in this question represent RGB (Red, Green, Blue, respectively) webcolours (html hex colours) that employ the hexadecimal counting system used in computer science. Hexadecimal numbers are a compact way of representing large numbers since they have a base of 16, instead of 10. They are useful in computer programming because computers use bytes as their main unit of information storage. Whereas it normally requires 8 binary digits to represent a byte, in hexadecimal only two digits are required.

Since we only have 10 numeric digits (0 to 9), hexadecimal also uses the letters A through F to represent the additional values of 10 through 15 (A-10, B-11, C-12, D-13, E-14, F-15). Each hexadecimal alphanumeric digit represents four bits ("BI nary digi TS"), also known as a "nibble". A pair of hexadecimal digits represents 8 bits, or one byte, with a value range of 00 to FF (0 to 255, or 256 "decimal" numbers).

In the RGB Colour System used in computers, there are 256 possible levels of brightness for each component in an RGB (Red, Green, Blue) colour. So the red, blue, and green light components are each represented by one byte, or two hexadecimal digits. An entire RGB colour can therefore be represented by six hexadecimal digits in the respective order #RRGGBB.

Of course, there are many websites that provide conversion tables, calculate averages, and list complementary colours for you, but if you are interested in the math behind these processes, we go into further detail below.

#FACE8D is a hex colour that has:

Red light component = FA = (15 × 161) + (10 × 160) = 240 + 10 = 250

Green light component = CE = (12 × 161) + (14 × 160) = 192 + 14 = 206

Blue light component = 8D = (8 × 161) + (13 × 160) = 128 + 13 = 141

#BADF00 is a hex colour that has:

Red light component = BA = (11 × 161) + (10 × 160) = 176 + 10 = 186

Green light component = DF = (13 × 161) + (15 × 160) = 208 + 15 = 223

Blue light component = 00 = (0 × 161) + (0 × 160) = 0 + 0 = 0

The average of these colours is:

Red light component = (250 + 186) ÷ 2 = 218 = DA

Green light component = (206 + 223) ÷ 2 = 214.5 → Rounding up = D7, Rounding down = D6

Blue light component = (141 + 0) ÷ 2 = 70.5 → Rounding up = 47, Rounding down = 46

So, based on whether we round up or down, the average colour can be either #DAD747 or #DAD646, with the difference being virtually indistinguishable to the eye:

Complementary colours are those that are found opposite from each other on the colour wheel, so the most accurate way to find a complementary colour mathematically is to use the HSL (Hue, Saturation, Lightness) Colour System that is based on the same colour wheel. The process involves converting the RGB component colour values to HSL values, then adding 180° if the answer is less than 180°, or subtracting 180° if it is equal to or greater than this value. Converting between RGB and HSL requires some funky math formulas (which can be found at: http://www.rapidtables.com/convert/color/rgb-to-hsl.htm and http://www.rapidtables.com/convert/color/hsl-to-rgb.htm). Luckily, these conversions are easily made using any number of handy online tools if you are not mathematically inclined.

Depending on how you rounded when you calculated the average of #FACE8D and #BADF00, you will find the hex complementary colour of #DAD747 to be #4649DA or #474ADA. Likewise, #DAD646 has a colour complement of #4649DA or #4549DA. These colours are all very close, with only very slight variations in the red or green components — the blue component remains the same.

The complementary colour has a blue light component of DA or 218, whereas #C0FFEE has a blue light component of EE or 238. The diffence of 20 is equal to about 7.8% (20/255).


 

Question for Wednesday April 17, 2013:

On February 15, 2013, a previously unknown meteor suddenly and unexpectedly exploded in the daytime sky near the Russian city of Chelyabinsk, generating a shockwave causing extensive damage and injuring more than a thousand people. This stepped up public interest in trying to detect as many near-Earth objects (NEOs) as possible. By doing so, the thought is that if a meteor is detected to be on a collision course with the Earth early enough, it might be able to have its trajectory altered so as to avoid disaster. In fact, NASA's budget for 2014 includes a plan to develop a way to robotically capture a small NEO and study ways to try and protect the Earth in the future. Of course, a big part of the problem is finding these objects in the first place.

Fast forward to the year 2020. You have been given a summer intern position at NASA's asteroid watch program. Earlier in the year, a colleague detected a new NEO - a 4 km diameter asteroid given a provisional designation 2020 RQ3. He figured out that this asteroid will approach the Earth very closely in 5 years, but the better that this object's orbit is determined, the more accurately that the likelihood of a collision can be predicted.

The best way to determine an object's orbit is to observe where it is at different times. You know where 2020 RQ3 was when it was discovered. Now that it's been a couple of months later, you took two pictures of the sky through a powerful telescope last night, about an hour apart from one another, in the general region of where the asteroid was expected to be. The idea is that the object that moves between the pictures is likely going to be 2020 RQ3 instead of one of the background stars. Be aware, that due to the Earth's atmosphere distorting the view unpredictably, and the fact that the telescope cannot be lined up precisely the same way when both photographs were taken, everything will seem to move a bit. You're looking for the object that moved significantly.

You also worked out regions in the sky where the asteroid would have to be now for various chances of a collision with the Earth in 5 years, and overlaid them on top of the two photos that you took. For example, if the asteroid is currently located in the ellipse labeled with 99%, it has a 99% chance of hitting the Earth at its closest approach 5 years from now. What would be the value on the Torino Scale for 2020 RQ3?

Acceptable answers:
6

Explanation:

The first step in solving this problem is to find out where the asteroid is in the star field. Though possible to find the object that moved by painstakingly going through the pair of photos bit by bit manually (somewhat reminiscent of a "Where's Waldo" puzzle), fortunately there is a quicker way.

Astronomers are often faced with the problem of finding what has changed between two photographs. They found that by rapidly switching from viewing one photograph to viewing the other, differences between the two can be quickly identified. A device called a "blink comparator" was invented to do so, so called because it "blinked" between viewing each of the two photographs. Blink comparators have been used extensively throughout astronomical history, perhaps most famously by Clyde Tombaugh in 1930 when he discovered Pluto using the device and associated technique, after searching through hundreds of such pairs of photographs for nearly a year.

Fortunately, in these days of computers, a bulky mechanical device is not necessary any more. All you have to do is somehow align the two pictures on your computer and flip between them. There are lots of ways to do this without requiring specialized software. One such way is to right click on each picture and load them into separate tabs in your web browser, and then flip between the tabs. Or, if you are unable to do so, you can also just load the question into two web browser windows, positioning the windows and their scroll location within to show each photograph in the same location of the screen, and then flip between them.

If you do so, you will end up seeing something like this:

Regardless of whether you use some method of blinking between the photos, or manual searching through them, you should have found our asteroid 2020 RQ3 located within the ellipse that designates a 0.5% chance of it hitting the Earth in 5 years.

Now, we have to figure out how this helps us classify the object on the Torino Scale. As can be found on the web, Torino Scale classification can be done with the following chart:

A 0.5% chance works out to a probability of 0.5 ÷ 100 = 0.005. In exponential notation, this can be rewritten as 5× 10–3. This is your horizontal axis position on the graph. The vertical axis shows kinetic energy in megatonnes, as well as approximate asteroid diameters that would yield such an energy. In our case, we're working with a 4 km diameter asteroid, so that's our vertical position on the graph. The two intersect at a Torino Scale classification of 6.

A 6 on the Torino Scale is defined as "threatening", and "A close encounter by a large object posing a serious but still uncertain threat of a global catastrophe. Critical attention by astronomers is needed to determine conclusively whether a collision will occur. If the encounter is less than three decades away, governmental contingency planning may be warranted." It's a good thing NASA is starting to seriously study how to affect the trajectories of such NEOs!


 

Question for Thursday April 18, 2013:

 

 

 

(In standard SI UNTZ, to the nearest 10TH, PLZ.  No UNTZ with final answer.)

Acceptable answers:
2.2
2.3
2.4
2.5

Explanation:

To decode this Canadian vanity license plate rebus you needed to "read" the plates using a combination of the number and letter names, as well as their phonetic sounds (much like the shorthand some people use when texting). Correct decryption reveals the following message:

Geeky Bumpers

Attention: physics teaser for you to decipher.

Calculate difference that gravity accelerates at surface of Neptune and Uranus.

May the force be with you.

(In standard SI units, to the nearest tenth, please. No units with final answer.)

To answer this question you needed to do a bit of research on the two mentioned planets. In the process, you may have discovered that there is some variation in the reported gravities of Neptune and Uranus. Let's try to understand why.

 

The acceleration due to gravity on the surface of any planet can be calculated directly from Newton's Law of Gravitation, which gives the formula:

g = GM/r2, where :

g = acceleration of gravity at a particular point

G = universal gravitational constant (or Newton's constant) = 6.67x10-11 Nm2/kg2

M = mass of the body

r = radius (distance from the center of the gravitating body to its surface)

Surface gravity is measured in units of acceleration, which, in the SI system, are meters per second squared.

Although gas giants may have a rocky or metallic core (such a core is thought to be required for them to form) the majority of their mass is in the form of hydrogen and helium gas.

Unlike rocky planets (like Earth), which have a clearly defined difference between atmosphere and surface, gas giants do not have a surface per se; their atmospheres simply become gradually denser toward the core. You could never "land on" such planets in the traditional sense. For this reason, the gas giants are harder to define with respect to their radius.

Bearing all of this in mind, the accelerations due to gravity on the surfaces of Neptune and Uranus are approximately 11.15 m/s2 and 8.69 m/s2, respectively.

The difference is therefore: 11.15 — 8.69 = 2.46 m/s2. Rounded to the nearest tenth, we accepted answers ranging from 2.2 to 2.5.


 

Question for Friday April 19, 2013:
 

prolific poet
 
 when it rains
 it really poors
 (1935... such a depressing time)
 fourteen rejections
 that was quite unb-e-c-o-m-i-n-g
 (especially since i was already an Enormous success)
 there must be a way
 wit persistence one prevails
 (thanks for the $300, mom)
 first, a title change
 then my work is off to print
 (my grasshopper composition nearly leapt off its page!)
 and the final nail in the urn
 really identified those who dismissed me
 (my dedication was a revelation)

What was the original title of the collection that was repeatedly rejected?

(Hint: Don't rely on just the wiki to solve this question... other resources will help you prevail!)

Acceptable answers:
70 poems
70 Poems

Explanation:

Edward Estlin Cummings, aka ee cummings (October 14, 1894-September 3, 1962) was an American poet and painter who attracted attention for his eccentric punctuation and typesetting. He often ignored the rules of capitalization and orthography in his works, and fittingly, a popular misconception about this author involves the way his name appears when written or typed. Some believed he had his name legally changed to lowercase letters, but his wife reported this to be untrue. Cummings did not object when publishers used only lowercase letters to write his name, but he himself capitalized his name in his signature and in the title pages of original editions of his books.

Cummings was a prolific artist who produced plays and portraits as well as books and poems. From the age of eight until he was 22, he wrote poetry daily. The specific work we refer to in this question is a compilation of poetry written during the depression era which was turned away by no less than 14 publishers. These rejections were conceivably even more upsetting to Cummings, given he had already established himself as a successful writer with his first autobiographical novel titled The Enormous Room (1922).

In any case, the repeated rejections didn't stop Cummings. Ultimately, he turned to his mother for financial assistance, and she gave him $300 to self publish this specific collection of poems in 1935 under his own imprint, the Golden Eagle Press.

In the end, Cummings decided to change the title of this book from the original "70 Poems" to the witty and indignant "No Thanks". This allusion was most certainly meant for those 14 publishers who had rejected his book. As a final dig, Cummings also used the first page to dedicate the book to them, arranging each of their names to form the shape of a funeral urn.

 

A well-known poem from "No Thanks" is titled "r-p-o-p-h-e-s-s-a-g-r" (grasshopper) and many interesting interpretations can be found online. One prevalent observation is that the poem was deliberately typeset to form the outline of a grasshopper. Others note how the letters playfully jump in and out of order, mimicking the insect's natural movements. (See images below.) This poem is one of many that epitomizes Cummings' unmistakable style. He wrote more than 2900 poems in his lifetime.

 

__________________________________________________


 

Question for Saturday April 20, 2013:

 

Disclaimer: This question is for fun and educational purposes only. The Noggin Hoggin' Challenge and ExamBank do not recommend the harvest and consumption of wild mushrooms by amateurs. Proper identification depends on multiple factors and enthusiasts should train under the tutelage of an experienced mushroomer to avoid costly (or fatal) mistakes. Please contact your local mycological society for more information.

You have carelessly ventured alone into the Canadian Rocky Mountains for a hike with neither a map nor a compass, and have gotten yourself thoroughly lost. Not expecting to be gone for long, you did not pack adequate supplies, but you have the good sense to make shelter and stay put (knowing that wandering around is only likely to take you further off course and make it harder for rescuers to find you). Thankfully, you did make a point of telling your friends where you were headed. You are also fortunate to find a clear stream nearby, and successfully start a fire.

Fast forward through four long, lonely days, with no luck finding food; you have gotten painfully and obsessively hungry. Although the tempting variety of wild mushrooms around your campsite has caught your eye on several occasions, you have wisely avoided them... until now.

Mad with hunger, you single out similar looking fungus pairs that share characteristics with mushrooms you believe to be edible; noting key differences between them. You are well-aware that consuming the wrong fungus will have terrible consequences — poisoning can range from serious gastric upset and confusion, to organ failure and death. As the old saying goes:

"There are old mushroom eaters and there are bold mushroom eaters, but there are no old bold mushroom eaters."

Which of each pair is the safest bet to cook and eat, with the least risk for complications?

0
1
Do you choose to cook and eat mushroom
0 or 1?
A
         
B
         
C
         
D
         

You notice that there are many bytes you can make out of this nibble if you add four more bits as below.

 (Hint: your mushroom choices above fill the blanks)

As your final answer, what is the SUM of the decimal values of all lower ASCII alphanumeric characters that end in the same nibble as above? (do not confuse lower ASCII with lower case)

Acceptable answers:
405
438

Explanation:

The mushrooms pictured in this question are:

0
1
Do you choose to cook and eat mushroom
0 or 1?
A
Golden Chanterelle
(Cantharellus cibarius)
→Edible
Jack O'Lantern
(Omphalotus illudens)
→Poisonous
0
B
Black Morel
(Morchella elata)
→Edible
False Morel
(Gyromitra esculenta)
→Poisonous
0
C
Common Puffball
(Lycoperdon perlatum)
→Edible
Destroying Angel
(Amanita ocreata)
→Poisonous
0
D
Fly Agaric
(Amanita muscaria)
→Poisonous
Northern Roughstem/Red Cap*
(Leccinum boreale)
→Edible
1

*A bill was actually passed in 2009 to make the Red Cap the official provincial mushroom of Alberta, although it cannot be law until an amendment is introduced to the Emblems of Alberta Act. This would make Alberta the only Canadian province with an official mushroom.

So, in order from A to D, the correct responses are 0, 0, 0, and 1.

In computer science, a bit is a unit of information often expressed as either a 0 or 1, in the internal language of computers — a system called binary notation. A nibble is a set of 4 bits, and a byte is 8 bits (or two nibbles) operated on as a unit.

If we treat 0001 as the last nibble and then add variables for the first 4 bits, then we end up with the following byte:

In computer science, ASCII (pronounced ask-ee) is the acronym for the American Standard Code for Information Interchange. It is a set of digital codes that use binary to represent printable characters and non-printable control characters (like "delete"). ASCII is widely used as a standard format in the transfer, processing, and storage of English language text files between computers and on the Internet (although its prevalence is slowly being replaced by UTF-8, which remains compatible with the lower ASCII code set and allows for standardization of accented letters as well as letters from other languages).

Originally binary numbers with seven digits (seven bits) were used, which made it possible to represent a total of 128 characters. The use of 8-bit numbers was later introduced, increasing the total to 256 characters. The first 128 characters are traditionally called "lower ASCII" characters, whereas the next 128 characters are termed "upper ASCII". Upper ASCII has been traditionally used to provide for accented letters and support for other languages, but has never enjoyed the standardization that lower ASCII has, which is why we are only asking for characters in the lower ASCII code set.

There are 5 alphanumeric (either a letter or a number) lower ASCII characters that end in the binary code 0001; they are listed below with their respective decimal values:

Character
8-bit Binary
Decimal
1
00110001
49
A
01000001
65
Q
01010001
81
a
01100001
97
q
01110001
113

Whereas the binary (base two) numeral system has only two possible values for each place-value, the decimal (base ten) numeral system we are more familiar with has ten possible values (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9) for each place value. Converting from binary to decimal is not that difficult - you just need to know the place value for each position, and these increase by a power of 2 from right to left:

27  26  25  24  23  22  21  20  =  128  64  32  16  8  4  2  1

So, for binary value 00110001 we get:

(0 × 128) + (0 × 64) + (1 × 32) + (1 × 16) + (0 × 8) + (0 × 4) + (0 × 2) + (1 × 1)
= 32 + 16 + 1
= 49 as a decimal value.

Of course, there are online calculators that can do this for you as well.

The sum of the decimal values of characters 1, A, Q, a, and q is:

49 + 65 + 81 + 97 + 113 = 405

There are, however, some online resources that take a less restrictive approach to defining alphanumeric characters, including punctuation along with letters and numbers. If this definition is used, then binary 00100001 (decimal 33, ASCII character '!') would be included. We therefore also accepted an answer of 33 + 49 + 65 + 81 + 97 + 113 = 438. Note, however, that binary 00000001 (decimal 1) and 00010001 (decimal 17) are not considered alphanumeric by any definition - they are known as control characters, and do not represent printable information.