Difference between revisions of "2018 AMC 10B Problems/Problem 14"
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== Solution == | == Solution == | ||
| − | To minimize the number of distinct values, we want to maximize the number of times they appear. So, we could have 223 numbers appear 9 times, 1 number appear once, and the mode appear 10 times, giving us a total of <math>223 + 1 + 1</math> = <math>\boxed{\textbf{(D) } 225}</math> | + | To minimize the number of distinct values, we want to maximize the number of times they appear. So, we could have <math>223</math> numbers appear <math>9</math> times, <math>1</math> number appear once, and the mode appear <math>10</math> times, giving us a total of <math>223 + 1 + 1</math> = <math>\boxed{\textbf{(D) } 225}</math> |
==See Also== | ==See Also== | ||
Revision as of 12:31, 17 December 2019
Problem
A list of 
positive integers has a unique mode, which occurs exactly 
times. What is the least number of distinct values that can occur in the list?
Solution
To minimize the number of distinct values, we want to maximize the number of times they appear. So, we could have 
numbers appear 
times, 
number appear once, and the mode appear times, giving us a total of 
= 
See Also
| 2018 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
| 2018 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 9 |
Followed by Problem 11 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
