Difference between revisions of "2018 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 3"
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== 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== | ||
− | + | 10 choose 3 = 120 | |
== See also == | == See also == |
Latest revision as of 03:56, 10 August 2023
Problem
Let be three positive integers in the interval
satisfying
and
. How many different choices of
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 |