Probability, Counting & Combinatorics
The Sprint Round of the MATHCOUNTS Chapter Competition has 30 questions and students are given 40 minutes to complete the round. Though it isn’t expected that most students will finish all 40 questions, what is the average time a student can spend on each of the 30 questions, in minutes:seconds per question?
The third Monday of January is the holiday commemorating the birthday of Martin Luther King, Jr. The first time Martin Luther King Jr. Day was celebrated was in 1986. Try to solve these problems without using a calendar!
How many times has Martin Luther King Jr. Day been celebrated?
In 1998, Nkem Chukwu gave birth to the first set of surviving octuplets. The eight babies weighed from 11.3 ounces to 28.6 ounces at birth. Leonard Weisman, the Texas Children’s Hospital’s chief of neonatal services, said it was imperative they gain lots of weight before they go home. “For instance, the 500-gram babies are going to have to quadruple their weight [to reach a healthy level],” he said. How many ounces will the heaviest baby have to gain to reach a healthy level?
While there were many problems written and solved for MATHCOUNTS in 2019, below is a selection of some of the best of the year!
2018-2019 School Handbook, #27
A segment with endpoints G(-2, 3) and H(4, 7) is dilated by a scale factor of 2/3 with center of dilation (0, 0). What is the sum of all the coordinates of G’ and H’?
Abby, Brenda, Celia, Denise and Elizabeth are going to their town’s annual hayride. Tickets cost $8.00 for people 12 years old and older but only $5.00 for people 11 years old and younger. The total price for their five tickets is $31.00. How many people in the group are 12 years old or older?
In honor of this year’s School Competition being released to registered competition coaches for our 2019-2020 Competition Series, see some of last year’s School Competition questions below!
Sprint Round, 19
Josie selected a number n. She divided n by 2 and then subtracted ½ from the result. She took half of that result and then subtracted ½ to get the final result of 10. What is the value of n?
Season 17 of American Idol ended earlier this year. At the end of the season finale, each of the three judges was asked to share his/her opinion about who should win the contest; Laine or Alejandro. Each of the three judges responded and audiences around the country basically heard “Laine,” “Laine,” “Laine.” If each judge answered either “Laine” or “Alejandro,” how many additional ways could the judges’ responses have been heard?
It’s probably a little strange to think that some students started school last week, some have another couple of weeks of summer vacation and still others are just continuing with their year-round school schedule! The date of the beginning of the school year has been a topic of debate throughout the last decade (and even before) in many areas across the United States. But the trend is definitely leaning towards starting school earlier rather than later. Basically, in the last 10 years, the percent of public schools going back to school before Labor Day has increased by 63%