By: Craig McPherson A 2021 Dodge Challenger SRT Hellcat Redeye, pitch black with bold red racing stripes (Credit : Exotic Motorsports of Oklahoma). The pony car era was the period of time between 1965 and 1973 when affordable, yet stylish and sporty cars would first be made and become popular. This includes the likes of the Ford Mustang and Chevrolet Camaro. But around the middle of this period, one competitor would rise, and it would have a fairly unique story compared to these other examples. This competitor would be none other than the Dodge Challenger. This is the story of how the Dodge Challenger revolutionized the world of muscle and racing in the auto industry. In 1967, Chrysler had predicted that the sales of “pony” cars would grow to 1.5 million by 1970. At this time, the company began work on a successor for their Plymouth Barracuda. It was meant to compete with the new Pontiac Firebird and Mercury Cougar. This successor, the original Challenger, was revealed to the world by 1970. While the Challenger heavily resembled the Barracuda, it was notably larger. It also had brand new features such as concealed windshield wipers, flush door handles, and molded polypropylene door panels. The original Dodge Challenger was also offered as a Road/Track, or R/T variant. The R/T had stiffer suspension, bigger brakes, and a more powerful engine. This engine was the legendary V-8 426 Hemi, with a staggering 425 horsepower. Initial sales were incredible, Dodge had sold nearly 80,000 Challengers. But sales would significantly fall after 1970, possibly due to the pony car era coming to a close. Production of the original Challenger would eventually end halfway through 1974, exactly 165,437 models were manufactured. During the late 70’s and early 80’s, smaller, more fuel efficient cars would take the popularity of the pony car. But for the sake of sales, companies would market new compact models with the names of their old, sporty models. Ford had done this with a design based on their Pinto, calling it the “Mustang II”. Dodge had done something similar in collaboration with Mitsubishi. Since 1971, Chrysler had been importing subcompact models from the Japanese company. In 1978, they would take a rear-wheel drive coupe, based on the Mitsubishi Galant, and sell it as the second generation Challenger in the United States. This new, smaller Challenger would be given a more spacious makeover in 1981. However, it was replaced by the Dodge Conquest in 1983. The Challenger’s next revival, and most recent chapter would begin in 2006. When the new design was first revealed, it was noted how the exterior managed to strongly resemble that of the original design of 1970. Not too long after, in 2008, the Challenger gained a popular new variant in the SRT8. The SRT8, like the original Challenger, had a Hemi V-8 engine with 425 horsepower. By 2015, the Challenger gained three more new variants, all branded as the R/T. This included the R/T Scat Pack, with 485 horsepower and the new TorqueFlight eight-speed automatic. The SRT8, meanwhile, was rebranded as the SRT 392, as they had a new, top performance muscle and racing model; the SRT Hellcat. The Hellcat was a major game changer since its debut, immediately becoming the strongest street legal car on the market. It had 707 horsepower, surpassing the 662 horsepower Ford Mustang Shelby GT500. There were very few changes to the Challenger’s design between 2015 and 2017. Aside from the introduction of an all-wheel drive Challenger with the Challenger GT. It also had the same suspension as the Dodge Charger Pursuit, a police car variant of the Charger. However by 2018, Dodge was able to make something even stronger than the Hellcat; the SRT Demon. The Demon could achieve as much as 840 horsepower, using a 2.7 liter supercharger, and a new valve train. It also had an automatic race cooldown feature that made it easier for the engine to cool down when racing. The Demon was specifically designed to be more ideal for drag racing. However, the Dodge Demon’s production was notably limited, only 3,300 of them were made annually. To compensate for this, Dodge would create the Hellcat Redeye in 2019. It was not as strong as the Demon, but still stronger than the original Hellcat, with 797 horsepower. It had similar wheels to the Demon, and a unique emblem; a glowing red eye. Dodge also made another drag racing focused variant known as the R/T Scat Pack 1320. It had many of the same features as the Demon, such as a TransBrake, cooldown, line lock, and a drag mode. In 2020, a more direct successor to the Demon was introduced with the SRT Super Stock. It had just slightly more horsepower than the Redeye, as it had recalibrated shift points. In conclusion, the Dodge Challenger was more than just Dodge’s attempt to hop on the pony car bandwagon. With this particular model, they were able to redefine drag racing, and create some of the most powerful engines to ever grace the street or the track. As members of the Challenger’s brain trust like to say; “We're very proud of the fact that at SRT, we don't speed-limit our products. They're governed by the laws of physics.”

By: Adith Bondugula As winter changes into spring, students are beginning to prepare for one of the most significant decisions of the year, course selection. While it may not seem like a big deal, the decision that students are making is very important and may have a great impact on their academics and possibly even their college career. For many upper-class students, this is a strategic process where one has to balance advanced courses, career interests, and personal passions all at once when picking courses. Students should try their very best to challenge themselves, but make sure not to be unrealistic and overload themselves with too many advanced courses. Advanced Placement and Honors courses are popular choices for students who want to prove they are able to handle challenging courses, but taking these courses means you have to generally be a more responsible student and put more effort and time into studying. Another important factor that decides what course a student may pick is what their future goals and career targets are. An example of this is if a student has any future goals of pursuing a career in the field of business, medicine, or engineering. The student may thus choose to pick a class that relates to the chosen field of interest they have. For instance, the student may have future goals of one day finding a job in the financial field and, for that reason, decide to pursue a course that is related to some kind of area in economics or business. Similarly, if a student may want to one day have a job in the field of technology, it is a good idea to take some kind of computer science course that gives them career skills such as coding and programming. Still, it might not be a good idea to base every class you take purely on academics, and it may be a good idea to take a class in an area you are not too familiar with in order to explore and learn more about other fields, even if you don't intend them to be a career focus. Also, students should make sure to weigh in if they have any important commitments that take up time after school, such as a sport, club, or work, when trying to come up with a successful combination of courses that will work out for them. While the schedule might look good when a college admissions officer looks at it on your application, it may be overwhelming in real life if a student is not able to spend the time they need to be successful in the courses they take and get good grades. Advice for Underclassmen It is especially difficult for freshmen and sophomores to choose courses. It is easy to overestimate or underestimate one’s abilities, as one does not have much experience. Here are some of the most important pieces of advice: 1. Make Sure To Challenge Yourself — But Be Realistic It’s perfectly fine if you take a few challenging classes, but don’t overdo it. It’s better to succeed at a good number of classes than to struggle at a lot of challenging classes. 2. Think Long-Term Think about the long-term effects of the classes you take. Some classes have prerequisites, so it’s a good idea to plan ahead. 3. Talk to Teachers and Counselors Teachers can provide you with advice about what a class is really like, and guidance counselors can provide you with advice about how you can plan a class load to help you meet your goals. 4. Don’t Just Follow Your Friends It’s tempting to sign up for classes with your friends, but you should sign up for classes based on your interests and abilities. 5. Leave Room for What You Enjoy Electives will give you time to look into new interests and will give you a break from other classes. Maybe you like art, music, or journalism. These classes can make your high school years a much more enjoyable time. Finding the Right Balance It is, at the end of the day, all about finding that balance. Course selection is not only about finding a schedule that is going to challenge a student, but also give them opportunities for growth outside of the classroom. When choosing a course for the following year, try to ask yourself if you genuinely are interested in what this class will teach you, as well as making sure you can handle the coursework it offers.

By: Craig McPherson A 1990 Ferrari F40 in Ferrari’s signature shade of red; Rosso Corsa (Credit: For Sale: Ferrari F40 (1990) - Classic Trader). Italy is one of the most prominent nations in the automobile industry. It is home to many beloved brands, Ferrari being one of them. Ferrari has crafted plenty of unique, beloved sports cars. Each one is fairly significant in its own right, but in terms of importance, one particular model arguably trumps them all. This particular model is none other than the F40. This is the story of the Ferrari F40, not just how it was conceived and evolved over time, but just what it did to influence the world of sports cars. The development of the F40 began as early as 1984. Ferrari wanted to develop a new GT, or Grand Touring, style car to compete in Group B. Group B was a series of rallying and racing challenges in Europe. To achieve this, Chief Engineer Nicola Materazzi suggested using the engine from the 288 GTO as a basis for the engine of a new model. Materazzi was allowed to make this design choice if he only worked on it during weekends. The result of these initial efforts would be the Ferrari 288 GTO Evoluzione, a direct successor to the original 288 GTO, in 1986. However, Group B had also ended by this time. Enzo Ferrari, founder and leader of Ferrari, was unsure of what to do with these new cars without a series for them to compete in. That is, until he agreed to allow Materazzi to keep the original design of the Evoluzione, but modify it to become street legal. The result of this new endeavor would be the original Ferrari F40 in 1987, the same year that the company would see its 40th anniversary. It had a unique, Tipo F120A engine, a 2.9 litre twin-turbo V8. This 478 horsepower engine enabled the F40 to reach speeds of 201 miles per hour. It was for this reason that the F40 not only rivaled cars like the Lamborghini Countach or Porsche 959, but it was also the fastest street legal car of its time. Unfortunately though, this was the last production of a new Ferrari overseen by Enzo, as he would pass away in 1988. However, this last project would be a great way to end his legacy. There would also be a few special racing editions of the F40 that were built later on, including the LM, Competizione, and GTE. However, the lifespan of the F40 would last for less than a decade, when production ended in 1996 with just slightly over 1,300 units manufactured. Despite this, the pure ambition and innovation that went into the Ferrari F40 more than earned its legendary status in the world of automobiles and racing. As Formula 1 designer for McLaren Gordon Murray said; “The best supercar ever made, and may ever be.”

By: Craig McPherson In my opinion, teachers should stop using Blooket to help students review curriculum materials because the game is poorly designed. One of the most commonly criticized aspects of Blooket’s game design would have to be that it prioritizes luck over knowledge. An example of this would be in the mode, “Gold Quest”. In it, players choose one of three treasure chests for each question they answer correctly. They can obtain a certain amount of gold from the chests, and the winner is whoever has the most gold at the end. The contents of each chest are seemingly random, and two possibilities include losing gold and the ability to swap gold with another player. This can be rather unfair because students who understand the materials, and answer more questions accurately, can still get unlucky and lose their gold. Meanwhile, other students who don’t understand the material, and perform worse, can simply get lucky and still end with more gold. Another reason that Blooket has poor game design would be that some aspects do not accommodate more sensitive or younger students. Elements such as the bright, oversaturated colors or loud music can be overwhelming for students higher on the spectrum. The time limit, which only allows a student at most a minute, to answer a question, can also be stressful. As an article on the pros and cons of Blooket said; “Many game modes reward fast answers, not just correct ones. This disadvantages kids who are still developing reading fluency or processing speed. A first grader who knows the answer but takes an extra few seconds to sound out the words will consistently score lower than faster readers, which can feel demoralizing” (Screenwise). Younger students who need more time to think before answering are generally less rewarded than students who answer more quickly. This can be damaging to the self-esteem of these more sensitive students. One last flaw with the game design of Blooket would be how it is notably easy to hack. A fairly accessible platform called GitHub enables students to download software that allows them to directly manipulate games. This means that a student could easily hack the game and gain unfair advantages, such as tricking the game into thinking they answer questions correctly when they actually do not, or gaining more points from questions than they are supposed to. Another way that this can be an issue is presented by the following quote from Anne Ogg, MEP Technology Facilitator for Millard Public Schools; “Around mid-April, Blooket was hacked twice during a middle school class, and the second instance displayed racist and hateful language,” (Prokupek). Not only are students using the hacks to cheat, but hackers can also use them to include highly offensive, explicit language in games for all classes to see. Overall, the game design is poor because it prioritizes luck over knowledge, it does not accommodate more sensitive or younger students, and it is notably easy to hack. In conclusion, teachers should stop using Blooket to help students review curriculum materials because the game is poorly designed. Therefore, teachers should refrain from using Blooket because although it’s a more interactive way to learn, it can cause more harm to a student’s learning process compared to other education methods.

By: Craig McPherson A portrait of Clara Barton, supposedly taken in 1866 (Credit: Wikipedia). March is not only Women’s History Month, but it is also national Red Cross Month. It only seems appropriate to discuss a woman who had a significant role in the history of the American Red Cross Organization. No woman could have a more important role in the organization’s history than its founder; Clara Barton. This article will not only honor her for her contributions to blood donations, but also explain her background and how she would create the Red Cross organization. Clarissa “Clara” Barton was born on December 25th of 1821. Growing up in Oxford, Massachusetts, she was the youngest of five and the daughter of a successful farmer. Her first experience as a nurse would be as a teenager, when she helped take care of her brother when he suffered a terrible head injury. When she was young, she was also notably shy. To help her become more outgoing, her parents encouraged her to become a teacher. To prepare for this, she studied at the Clinton Liberal Institute in New York. Barton began her career as a teacher when she was 18. She eventually established the first free school in Bordentown, New Jersey in 1852. However, her career would end when she was replaced as the school’s principal by a man. Besides being demoted to his assistant, Barton had to endure a poor work environment and a nervous breakdown, leading her to quit. Her next career began in 1854 as a recording clerk in the U.S. Patent Office. She was the first woman to ever work for the federal government, and her pay was the same as her male colleagues. Unfortunately, she still suffered abuse and hostility from her male counterparts, and eventually had her salary reduced before being fired not very long afterwards. In 1860, however, she did return as a copyist for a brief period. She did so to hopefully encourage more women to serve in the government. Clara would leave the Patent Office again in 1861, during the start of the Civil War. She did so to assist Union Soldiers by providing them with medical care and providing them supplies. It was because of this that she was famously dubbed “Angel of the Battlefield”. After the war, she would help over 20,000 missing soldiers reunite with their families. She also gave lectures about her experiences all over the U.S. from 1865 to 1868. As a result, Barton was noted to be an associate of Susan B. Anthony, and became an advocate for both Women’s Suffrage and Civil Rights. However, her activities over these few years would cause her to feel mentally and physically exhausted. Her doctor recommended she take a vacation. Therefore, in 1869, she took the trip to Geneva, Switzerland, where she first learned about the International Red Cross Organization. When Barton returned to America, she would gain support for the creation of an American Red Cross by educating people about the concept of the blood donation program. She would do so by writing pamphlets, giving lectures, and gaining the support of the President at the time, Rutherford B. Hayes. All of her efforts would pay off in 1881 when the American Association of the Red Cross was opened. Clara Barton served as the President of the association for 23 years, until 1904. She would pass away only 8 years later, on April 12th of 1912. To conclude, Clara Barton was not only a major historical figure in American medical practice, but also an excellent example of a feminist role model. Despite constantly facing sexual adversity and hostility from men, she always advocated for gender equality and became a significant figure in every field she worked in. As Barton herself once said; "I may sometimes be willing to teach for nothing, but if paid at all, I shall never do a man's work for less than a man's salary."

St Patrick's Day is a lively celebration that honors Irish culture and heritage. Every year on March 17th, people around the world join in to remember St Patrick, the patron saint of Ireland, and enjoy a day full of fun traditions and activities. The History of St Patrick's Day St Patrick's Day began as a religious feast day to honor St Patrick, who lived in the 5th century. He is credited with bringing Christianity to Ireland and is famous for using the shamrock to explain the Holy Trinity. Over time, the day evolved into a broader celebration of Irish culture, especially among Irish immigrants in the United States. The holiday became popular worldwide, with parades, music, and festivals marking the occasion. Today, it is a day to celebrate Irish heritage, whether or not someone has Irish roots. Traditional Symbols and Customs Several symbols are closely linked to St Patrick's Day. The shamrock, a three-leaf clover, is the most famous. It represents luck and the teachings of St Patrick. Another common symbol is the leprechaun, a mischievous fairy from Irish folklore, often shown with a pot of gold at the end of a rainbow. Wearing green is a key tradition. This color is associated with Ireland, known as the Emerald Isle, and is believed to make you invisible to leprechauns who like to pinch anyone they can see. Fun Traditions to Try High school students can enjoy many fun activities on St Patrick's Day. Here are some popular ideas: Attend or watch a parade : Many cities host parades featuring bagpipers, dancers, and colorful floats. If there isn’t one nearby, watching a parade online can be just as exciting. Cook Irish food : Try making traditional dishes like soda bread, corned beef and cabbage, or Irish stew. Cooking together can be a fun way to learn about Irish culture. Wear green and decorate : Dress in green clothes and decorate your room or classroom with shamrocks, rainbows, and gold coins. Listen to Irish music : Folk songs and traditional Irish tunes create a festive atmosphere. You can find playlists online or watch live performances. Play themed games : Organize a scavenger hunt for shamrocks or leprechaun gold, or try Irish dancing with friends. Table with traditional Irish food and green decorations for St Patrick's Day How to Make the Day Special Besides the usual celebrations, students can add their own twist to St Patrick's Day. Creating handmade cards with Irish blessings, learning a few words in Gaelic, or watching movies about Ireland can deepen the experience. Volunteering for a community event or sharing stories about Irish history also brings meaning to the day. St Patrick's Day offers a chance to have fun while connecting with a rich cultural tradition. Whether through food, music, or games, students can enjoy a day full of joy and learning.

Preparing for the New Jersey Graduation Proficiency Assessment (NJGPA) can feel overwhelming for many high school students. This test plays a crucial role in demonstrating readiness for graduation by assessing key skills in language arts, mathematics, and science. Knowing how to approach the NJGPA, understanding what counts as a passing score, and learning what to do if you don’t pass can make a big difference in your confidence and results. Student concentrating on NJGPA test materials Students preparing for the NJGPA test with focused study materials What the NJGPA Tests and Why It Matters The NJGPA measures proficiency in three main areas: Language Arts Literacy : Reading comprehension, writing skills, and understanding of grammar. Mathematics : Problem-solving, algebra, geometry, and data analysis. Science : Understanding scientific concepts, experiments, and data interpretation. Passing the NJGPA is a graduation requirement in New Jersey. It shows that students have mastered essential skills needed for college, careers, and everyday life. Schools use the results to identify areas where students may need extra help before moving forward. Understanding the Passing Score Each subject on the NJGPA has a specific passing score set by the New Jersey Department of Education. Generally, students must score at least 250 on each section to pass. Scores range from 100 to 300, with 250 representing proficiency. Here’s what the scores mean in simple terms: Below 250 : The student has not yet demonstrated proficiency in that subject. 250 or above : The student meets the proficiency standard. Schools provide score reports that break down strengths and weaknesses, helping students understand where they did well and where improvement is needed. How Students Should Approach NJGPA Testing 1. Start Preparing Early Waiting until the last minute to study can increase stress and reduce performance. Students should: Review class notes and textbooks regularly. Practice sample NJGPA questions available online. Focus on weaker subjects to build confidence. 2. Develop Good Test-Taking Habits On test day, habits can impact results. Students should: Get a good night’s sleep before the test. Eat a healthy breakfast to maintain energy. Arrive early to avoid rushing. Read each question carefully and manage time wisely. 3. Use Practice Tests Taking full-length practice tests simulates the real experience. This helps students: Get familiar with the test format. Identify question types that are challenging. Build stamina for the testing period. 4. Ask for Help When Needed Teachers, tutors, and counselors can provide valuable support. Students should: Attend review sessions. Ask questions about confusing topics. Use school resources like study groups or after-school help. NJGPA practice test materials ready for study Practice tests help students build confidence and improve skills before the NJGPA What to Do If You Don’t Pass Failing one or more sections of the NJGPA can feel discouraging, but it is not the end of the road. Students have options to meet graduation requirements: Retake the Test Students can retake the NJGPA during scheduled testing windows. It’s important to: Review feedback from the previous test. Focus on areas that need improvement. Use additional study resources. Alternative Assessments New Jersey offers alternative ways to demonstrate proficiency, such as: Portfolio Appeals : Students compile work samples that show mastery of skills. Other Standardized Tests : Some students may qualify to use scores from tests like the SAT or ACT. Local Assessments : Schools may provide district-level tests aligned with state standards. Seek Academic Support If a student struggles repeatedly, schools often provide: Targeted tutoring programs. Summer school courses. Individualized learning plans. These supports help students build the skills needed to pass the NJGPA or alternative assessments. Tips for Staying Motivated Preparing for the NJGPA can be stressful, but staying motivated is key. Students should: Set small, achievable goals for study sessions. Celebrate progress, not just the final score. Remember that passing the NJGPA opens doors to graduation and future opportunities. Talk to friends or family for encouragement. Final Thoughts The NJGPA is a significant step toward graduation, but with the right approach, students can succeed. Understanding the passing score, preparing early, practicing regularly, and seeking help when needed all contribute to better outcomes. If a student does not pass, there are clear paths to meet graduation requirements through retakes and alternative assessments. Students should view the NJGPA as a chance to show what they know and to identify areas for growth. With focus and support, they can navigate the NJGPA confidently and move closer to their goals.

Chika Ofili, a Nigerian boy, 12-year-old living in London just discovered a new Formula for divisibility by 7 in maths. Multiply the last digit by 5 and add it to the remaining numbers. For Example 532 53+2 x 5 = 63 which is a multiple of 7. So, 532 is divisible by 7. Chika Ofili has been presented with a special Recognition Award for making a new discovery in mathematics. A Proof for his Discovery: If x+5b=0 mod 7 then multiplying by 10 we get 10x+50b=0 mod 7. But 50 is just 1 mod 7 so we get 10x+b=0 mod 7 as an equivalent statement.

Cicadas are large insects that appear periodically in massive numbers. They are known as a symbol of resurrection because of their interesting life cycle, based on prime numbers. Cicada in Princeton, NJ Although Cicadas spend most of their life underground, they eventually have to come up to the surface for sunlight and reproduction. While on the ground, these insects mate and lay their eggs on tree branches. These eggs then take about 6-7 weeks to hatch, after which they burrow into the soil and continue this life cycle. However, when Cicadas do emerge at the surface, there are many dangers awaiting. These insects are easily eaten by birds, bats, spiders, wasps, and the list goes on and on. You may be wondering how this species has not gone extinct yet, as it has so many predators. This is where the prime numbers come into play. Cicadas that leave their underground habitat within a year or two are quickly devoured by scavenging predators. However, this doesn’t mean that the longer they remain underground, the longer they survive. Some Cicadas that don’t come up to the surface for 15 years or 18 years still get eaten faster than those that emerge in 13 years or 17 years. How is this possible? Periodical cicadas have the longest life cycle, coming up every 13 or 17 years, longer than an annual cicada in comparison. Due to these specific prime number life cycles, predators find it very difficult to catch these types of periodical cicadas. Prime Numbers: Prime numbers are whole numbers greater than 1 that cannot be divided exactly by any positive integer other than itself and 1. Every single number can be written as the product of prime numbers and every integer larger than 2 can be written as the sum of two prime numbers. How do these prime number properties relate to the cicadas’ life cycle though? Cicadas are not the only living species with their own unique life cycle. Their predators also have one, which can be 3, 4, 5, 6, or any number of years long. Take the wasp for example, which has a life cycle of 4 years. This means that every 4th, 8th, 12th, and so on year, the cicadas will be open to being eaten by the wasps. What if the cicadas had a life cycle of 8 years? They will be vulnerable to any predators blossoming on a 1, 2, 4, or 8 year cycle. Since their predators have shorter life cycles, they prey on cicadas the year that is a multiple of the # of years in their life cycle. So with prime #s, there are fewer chances of the predator life cycle to align with the cicadas cycle. Cicadas with a 12 year life cycle have the least chance of surviving the longest because of 12 has many factors, 1, 2, 3, 4, 5, 6, 12. Predators with any of these life cycles can catch cicadas. If the predator has a 2 year cycle, they will catch them every 6th year since 2 x 6 = 12. If the predator has a 3 year cycle, they will catch them every 4th year since 3 x 4 = 12. This pattern repeats for all of the factors. Using this strategy, cicadas have evolved to emerge every 13th or 17th year. There are many predators with life cycles between 2-12 years without a factor aligning with 13 or 17. For example if the predator has a 7 year cycle, they have a smaller chance of catching the 17-year cycling Cicadas since 7 x 2 = 14 and 7 x 3 = 21, skipping over 17. Using this method, the same result can be found for 13-year cycling Cicadas. Why don’t Cicadas survive as much in other prime number years? The reason for this is that if these insects emerge before 13 years, like in 11 years, then starving predators awaiting their arrival quickly finish them. If they wait for more than 17 years, like 19 years, then predators would have finished and digested their last meal, ready to eat the next round of Cicadas. Let’s use a predator with a 6 year life cycle as an example. With a 13-year cycling Cicada, the probability of the insect getting caught is 6 x 13 = 78 years, while with a 17-year cycling Cicada, the chance would be 6 x 17 = 102 years. This is a much longer span than if the life cycle was not following this prime number method. Another way these prime numbers 13 and 17 prove to be useful includes the rare chance of any of these periodically rotating species to interbreed with non prime number cycling breeds. For example, cicadas breeds with life cycles 8 and 10 have a much larger chance of interbreeding and mixing species. Multiples of 8 include 8, 16, 24, 32, 40, 48, 56, 64, 72, and 80. Multiples of 10 include 10, 20, 30, 40, 50, 60, 70, and 80. This means these two breeds of Cicadas will interact and emerge on the ground level together every 40 years, which is often. On the other hand, breeds of this insect with cycles of 13 and 17 interact much less often. Being prime numbers, they don’t have any common multiples until their product, 221. This means that these two breeds of Cicadas won’t interact for 221 years. The last time both of these breeds interacted amongst each other was in the year 2015, which makes the next time they emerge together the year 2236, 221 years from 2015. Clearly, prime numbers play a huge role in the evolution of Cicadas. Math is useful not only for our species, but even in nature for insects as small as Cicadas.

In 1975, Steve Selvin sent a letter to the American Statistician posing a probability brain teaser to his respondent. Little did he know, this one problem would be one of the most controversial problems to ever exist! What is this problem that stumped most of the world? Let’s say you are on a game show. You are given the choice of three doors: 1, 2, and 3. Behind one door is a brand new car and behind the other two are goats. Your goal is to attempt to choose the door leading to the new car. Whichever door you choose to start, Monty Hall will always open a different door, one with a goat. Suppose you start by choosing Door 1. He will open either Door 2 or 3, whichever leads to a goat. If both do, he will pick one randomly. Now two doors will remain, 1 and 2. The question remains, will you stick to your previous plan and choose Door 1 or switch your answer to the other closed Door 2? Which door would maximize your chances of picking the car? Why was this problem so difficult, though? Most people don’t use conditional probability, the chances that an outcome could occur after another event occurs, when approaching this problem. Instead, they attempt to formulate the answer without thinking it through step by step. Visual Approach: If you think about it visually, if you start by picking a goat, then Monty Hall will reveal the other door with the goat, so to win the car in that case, you have to switch to the other closed door. However if you start with a car, you must stay on that door to win. There is 2⁄3 of a chance you start with a goat and 1⁄3 chance you start with a car. Therefore, it is more likely you will win if you switch your answer to the other unopened door after Monty Hall opens one door. Conditional Probability Approach: To put this in a more mathematical way of thinking, let’s revisit Bayes' Theorem that we previously talked about in this Math Magazine, a very important topic in conditional probability. As a reminder, Bayes’ Theorem is a mathematical formula that can be used to calculate conditional probability for a test result, including the likelihood of a result based on a past result with similar circumstances. Formula: P(H|E) = P(E|H)P(E)P(H) In this case, H (hypothesis) represents door 1 leading to the car and E (evidence) represents Monty Hall revealing a door with a goat. P(H|E) represents the conditional probability of H, given E. So, let’s break this down into separate steps to think through this process more efficiently and understand it properly. P(H) - Since we still have no information or clues to predict which door will lead to the car, the probability of door 1 having the car will be the same as doors 2 and 3. So, P(H) = 13. P(E) - Since Monty Hall always picks a door leading to a goat, we already know this outcome. So, P(E) = 1. P(E|H) - For this variable, we can assume our H, door 1 having the car, is correct and when calculating the probability of E occurring, we know it will always happen. So, P(E|H) = 1. P(H|E) = (1)(1)(13) = 13 By using this formula, it can be concluded that multiplying the probability of the evidence occurring had no impact or change on the original probability of H, door 1 having the car. However, when looking at the other perspective of door 2 having the car, the probability will be double than that of door 1 since the car can only be in two doors after Monty Hall reveals one with the goat. The probability of door 2 will equal 26. Therefore, switching your answer to the other closed door after Monty Hall reveals one door will maximize your potential to get the problem right!