Difference between revisions of "1990 AIME Problems/Problem 13"
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== Problem == | == Problem == | ||
− | Let <math>T = \{9^k : k ~ \mbox{is an integer}, 0 \le k \le 4000\}</math>. Given that <math>9^{4000}_{}</math> has 3817 [[digit]]s and that its first (leftmost) digit is 9, how many [[element]]s of <math>T_{}^{}</math> have 9 as their leftmost digit? | + | Let <math>T = \{9^k : k ~ \mbox{is an integer}, 0 \le k \le 4000\}</math>. Given that <math>9^{4000}_{}</math> has 3817 [[digit]]s and that its first (leftmost) digit is 9, how many [[element]]s of <math>T_{}^{}</math> have 9 as their leftmost digit?hii |
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Revision as of 13:52, 28 October 2018
Problem
Let . Given that has 3817 digits and that its first (leftmost) digit is 9, how many elements of have 9 as their leftmost digit?hii
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Since has 3816 digits more than , numbers have 9 as their leftmost digits. Readdd
See also
1990 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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