Difference between revisions of "1993 AHSME Problems/Problem 16"
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== Solution == | == Solution == | ||
− | You want to find the largest integer | + | You want to find the largest integer <math>n</math> that satisfies <math>\frac{n(n+1)}{2}<1993</math>. |
− | + | ||
− | <math>\ | + | By trial and error, the value of <math>n</math> is <math>62</math>. Therefore, the next value of the sequence is <math>63</math>, and <math>63 \div 5</math> has a remainder of <math>3</math>. |
+ | |||
<math>\fbox{D}</math> | <math>\fbox{D}</math> | ||
Revision as of 22:15, 27 May 2021
Problem
Consider the non-decreasing sequence of positive integers in which the positive integer appears times. The remainder when the term is divided by is
Solution
You want to find the largest integer that satisfies .
By trial and error, the value of is . Therefore, the next value of the sequence is , and has a remainder of .
See also
1993 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 16 | |
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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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