Difference between revisions of "2018 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 3"
(Created page with "== Problem == Let <math>a_1 < a_2 < a_3</math> be three positive integers in the interval <math>[1,14]</math> satisfying <math>a_2-a_1>=3</math> and <math>a_3-a_2>=3</math>....") |
m (→Problem) |
||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| − | Let <math>a_1 < a_2 < a_3</math> be three positive integers in the interval <math>[1,14]</math> satisfying <math>a_2-a_1 | + | Let <math>a_1 < a_2 < a_3</math> be three positive integers in the interval <math>[1,14]</math> satisfying <math>a_2-a_1\ge3</math> and <math>a_3-a_2\ge3</math>. How many different choices of <math>(a_1,a_2,a_3)</math> exist? |
| − | |||
== Solution== | == Solution== | ||
Revision as of 12:38, 6 June 2022
Problem
Let 
be three positive integers in the interval ![$[1,14]$](http://latex.artofproblemsolving.com/f/2/c/f2c5505caae098da304b7d7f19acb6b60f500d32.png)
satisfying 
and 
. How many different choices of 
exist?
Solution
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 | ||
