Dear Math Circler,
Join us at Bard College on Wednesday, February 13, 2019 for the AMC 10/12 B contests. The event starts at 4 pm and will finish by 7 pm.
This event is free, but space is limited. Please register in advance.
Our favorite problem from last year's contest:
5. How many subsets of {2, 3, 4, 5, 6, 7, 8, 9} contain at least one prime number?
(A) 128 . (B) 192 . (C) 224 . (D) 240 . (E) 256
See below for a solution.
What are the AMC 10B and 12B?
The American Mathematics Competitions are a series of examinations that build problem-solving skills and mathematical knowledge in middle and high school students. Each of the AMC 10 (grades 10 and below, under 17.5 years of age) and AMC 12 (grades 12 and below, under 19.5 years of age) contests is 25 multiple choice questions long and runs for 75 minutes. The contest problems are accessible, yet go above and beyond the high school curriculum in both depth and level of challenge. To enjoy the AMC experience and grow mathematically, students are recommended to prepare, for example by solving past AMC 10 and AMC 12 contest problems.
The Bard Math Circle offers the B version of the exams on February 13, 2019. (The A version runs the week before on February 7.)
Join us after the contest for refreshments, and a mathematical conversation.
We can't wait to see you at the AMC 10/12B!
Bard Math Circle
A solution to our favorite problem from last year's contest:
There are 8 elements in the set {2, 3, 4, 5, 6, 7, 8, 9}, so 2^8 = 256 subsets in all. Instead of counting how many subsets contain at least one prime number, it's easier to count the complement: how many contain no prime number.
A subset contains no prime number exactly when it's a subset of {4, 6, 8, 9}, and there are 2^4 = 16 such subsets. Therefore, the number of subsets with at least one prime number is 256 – 16 = 240, which is option (D).
SUPPORT THE BARD MATH CIRCLE
Are you interested in donating to the Bard Math Circle?
Visit https://www.annandaleonline.org/mathcircle and make a donation.
Help support math enrichment in the Hudson Valley!