Probability, Counting & Combinatorics
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?
How many times since 1986 has Martin Luther King Jr. Day actually been celebrated on his birthday, January 15th?
What is the probability Martin Luther King Jr.’s actual birth date falls on the third Monday in January?
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%
The Walton and the Brady families plan to vacation together in an 8-bedroom vacation home. John and Olivia will bring six children — boys, Jason, Ben and Jim-Bob, and girls, Mary Ellen, Erin and Elizabeth. Mike and Carol also will bring six children — boys, Greg, Peter and Bobby, and girls, Marcia, Jan and Cindy. John and Olivia will sleep in one of the bedrooms, and Mike and Carol will stay in another bedroom. Each of the remaining six bedrooms each will be occupied by a pair of children, with six boys using three bedrooms and six girls using three bedrooms.
Thursday is the 4th of July... here are a few problems relating to Independence Day!! While walking around at their town’s Independence Day Festival, Latrease and Hannah decide to buy lunch. Latrease bought two hot dogs and a soda for a total of $7.50. Hannah bought a hot dog, a soda, and a bag of chips for $5.50. If a bag of chips costs $1.00, how much does one hot dog cost?
At Walter Whitman Middle School, to celebrate the last day of school, Mrs. Hanks brought in treats for her class. She has chocolate bars, lollipops and gumballs. Mrs. Hanks tells each student they can choose any combination of three treats from what she has. How many different combinations of three treats can one of her students chose?