Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2018 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 3

Problem

Let $a_1 < a_2 < a_3$ be three positive integers in the interval $[1,14]$ satisfying $a_2-a_1\ge3$ and $a_3-a_2\ge3$. How many different choices of $(a_1,a_2,a_3)$ exist?

Solution

10 choose 3 = 120

See also

2018 UNM-PNM Contest II (Problems • Answer Key • Resources)
Preceded by
Problem 2 		Followed by
Problem 4
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10
All UNM-PNM Problems and Solutions
Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2018_UNM-PNM_Statewide_High_School_Mathematics_Contest_II_Problems/Problem_3&oldid=196725"