Junior Math Olympiad
50 Exercises to review the Basics and get started strong
1st Edition
Published on 18. March 2026
60 pages
979-10-983393-6-3 (ISBN)
Description
Are you ready to take on the challenge of a math competition? Whether you are aiming for the Junior Olympiads, preparing for selective high school entrance exams, or simply want to master the fundamentals with rigor, 50 Exercises to review the Basics and get started strong Vol 1 is your essential companion.
This book is specifically designed to bridge the gap between classroom learning and the elevated thinking required in competitive mathematics. It focuses on reinforcing core concepts while introducing students to the types of problems that demand logic, creativity, and precision.
Inside, you will find:
50 Carefully Selected Exercises: Each problem is chosen to test and solidify the essential topics from the end of middle school and the beginning of high school .
Comprehensive Coverage: The exercises span key areas such as algebra, geometry, number theory, and logic, ensuring a well-rounded revision.
Step-by-Step Solutions: Every single exercise is accompanied by a detailed correction. You won't just find the final answer; you will learn the logical pathway to get there, understand the problem-solving strategies involved, and discover tips to avoid common pitfalls.
This book is perfect for motivated students looking to challenge themselves, as well as for teachers seeking high-quality practice material. Use it to strengthen your mathematical foundation and build the confidence needed to excel in any competition.
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CHAPTER 1: Where Did I Come From? Genealogy has a gravitational pull of curiosity for many folks wanting to know their roots. It fosters questions such as: Were our ancestors heroes or bandits? Did the family come from Royalty? Are there relatives nearby whom the family was unaware of and never met? As I write this book, none of these mysteries have ever much captured the interest of our two busy and loving children. Except for occasionally asking about an anecdotal family story, our children have displayed little genuine concern for their lineage or for any deeper understanding of their parents' days of youth. It is easy to understand this normal preoccupation with their own struggles in raising their families, developing their careers, and managing their marital relationships. It is also impractical to expect them, at this busy time in their lives, to be yearning to know our thoughts, fears, the awkward navigation of our teenage years, or how I felt when I strapped into the seat of my B-52 bomber as I prepared to fly another mission during the Vietnam War. This does not infer any flaws or shortcomings in their characters whatsoever! It just "IS what it IS." A celebrated author once advised me that my book must be my story. It cannot be anyone else's. He said: "If you think you're writing a book that's 'never been written,' you're kidding yourself." And, he expressed the critical importance of accuracy and honesty. Another respected writer told me: "You can write a good book poorly and still have a good book. But a good writer can produce a bad book if the writer does not have anything to say. If you are a good storyteller, you can produce a good book." I hope this book has something worthwhile to say that incorporates honesty, accuracy, and tells a good story with a purpose. For how can we know who we are and where we are going if we don't know anything about from where we have come and what we have been through, the courage shown, the mistakes made, the cost paid, and what brought us to be where we are? I fear that one day, such curiosity just might stir inside my children and grandchildren after I am gone. In that chance, I feel compelled to write the memoires of my youth so that I can share these stories with my offspring and their families. To anyone reading this book outside my family, I assure you that I am not writing this book to preserve my legacy, for my experiences are no more important than anyone else's. I just want my children, my grandkids, and beyond to know who I was and how I lived my life. The Brant Heritage I am sure that I am just one of many human beings grateful to and proud of their ancestors who made sacrifices, took risks, and paved the way for better lives for future generations. My grandfather, Walter Leon Brant I, came to Indianapolis on the final leg of his father's well-drilling odyssey that had slowly migrated west, as America thirsted for oil during the last half of the 19th century. Charles Pierson "C.P." Brant, Walter's father (and my great-grandfather), was orphaned at the age of nine when his father, Captain John Richard Brant of the 134th Pennsylvania Volunteer Infantry, was killed in the Civil War at the Battle of Chancellorsville (Virginia) in 1863, and his widowed mother died the following year. As a youngster growing up in Butler County Pennsylvania, he secured various jobs and learned several trades and skills that catered to the crude oil industry that was booming in western Pennsylvania at the time. After graduating from high school, C.P. worked in the oil fields as a laborer for his uncle George Brant. When George retired, C.P. ventured out on his own and built the Brant Oil Well Company, punching holes into the earth and erecting well riggings for the oil companies. As the Pennsylvania oil deposits began to draw down, C.P. and his wife, Luella (Ritts) Brant, moved his company to Lima, Ohio, where they had two sons, Walter and John. In 1898, they moved to Bluffton, Indiana, and in 1900 they moved to Indianapolis, where their third son, Charles Pierson Brant II, was born. Indianapolis proved to be a centralized locale to better oversee C.P.'s company projects in Illinois, Indiana, and Ohio. During the next three decades, C.P. had many gas and oil assignments, including jobs in Texas, Oklahoma (Indian Territory, as it was called then), Kansas, and Iowa. I need to interrupt the family history at this point and mention that, when I was a youngster, Sunday dinner at our house usually included my parents, sisters, and my grandfather Walter ("Grandpaw") and his wife, Bea ("Nanny"), gathered around the dining room table. It was a great time for Grandpaw to reminisce and tell stories of his youth. He told me of the time he actually traveled to the "Wild West" to "Indian Country" in a stagecoach hauled by teams of horses. Although the details and veracity are questionable, nonetheless he claimed to have accompanied his mother in 1890 to meet up with his father, C.P., who was working in the oil fields of the Oklahoma Territory. (Oklahoma did not become a state until 1907.) According to my grandfather Walter, at one of these rest stops in a one-street town, there was a gathering of people in the middle of the dusty street. Walter dashed away from Luella to see what was causing this huddle of onlookers. Walter weeded his way through the crowd and saw a man kneeling in the street with both hands holding his midsection. Blood oozed between his fingers and onto his pantleg. He had been shot in the stomach from a showdown gunfight, just like in a Western movie. No pictures or account of this trip to the "Wild West" survives, so the accuracy of his account is unknown; I only knew that my grandfather was not usually a person to make up tales. C.P. traveled a lot as Walter was growing up. As the eldest of the three boys, he was leaned upon to be the patriarch of the house in C.P.'s absence. Walter (nicknamed "Banty" or "Walt") attended Emmerich Manual High School where he played basketball and was an honor student. He was dedicated to his studies and took extraordinary lengths to stay out of trouble. During three of his high school summers he attended Culver Summer Naval School where he was toughened up, being subjected to some rough discipline administered by the upper classmen. Walter at Purdue University Walter excelled in math and physical sciences and went on to attend Purdue University in West Lafayette, Indiana. Although he was a dedicated student, he was always looking for mischief and a good time outside the classroom. He helped charter the Delta Tau Delta Fraternity house on campus, and his scrapbooks indicated that he attended a lot of dances and was quite a ladies' man. Purdue football games were the highlight of the Fall semester, especially before the annual rivalry with Indiana University. Grandpaw's favorite dinner-time lores usually involved his fraternity brothers. One such story involved the massive bon-fire at the pep rally the night before the IU game. The prior night, students would scour the area for wood to stoke the fire, stealing from local residential woodpiles, and tearing down outhouses, fences, etc. As this vandalism occurred this particular moonless night under the cloak of darkness, one of my grandfather's fraternity brothers fell into an open outhouse pit that only the previous day had been covered by an outhouse that had been dismantled just minutes earlier by other student-vandals. The brother sank to his armpits in indescribable human sludge, and when pulled to safety, had to be hosed down and his clothes burned. Purdue University buildings were powered by a coal-fired plant in the center of the campus. To get coal from the main railroad line that ran to the west of the campus, the university had its own steam locomotive and coal cars to transport the coal from the main rail line through campus to the power plant. Coincidentally, running through the campus was a trolley line that transported students throughout the campus as well as moving students and other passengers across the Wabash River to and from West Lafayette and the city of Lafayette. One evening, a few of Walter's fraternity brothers devised a grand scheme to steal the Purdue steam locomotive and drive it into Lafayette. The trolley tracks were the exact gauge (width) of the standard railroad tracks. After disconnecting the coal cars from the engine, the brothers rolled the locomotive to the intersection of the university train tracks and trolley tracks, flipped the switch, and eased the huge locomotive onto the trolley line. The steam engine slowly rolled through the center of West Lafayette and across the Wabash River bridge. As the locomotive approached the Lafayette courthouse square, the trolley tracks made a 90-degree right turn onto 3rd street. The sharp turn proved too abrupt for the six huge drive wheels, and the locomotive ground to a halt. Thinking perhaps more speed would assist in making the turn, the brothers backed up the locomotive and opened the throttle. The huge locomotive revolted at the thought of such a sharp turn and jumped the tracks, skidding to a crunching stop twenty yards up Columbia Street. Like a beached whale,...
