Difference between revisions of "1989 AJHSME Problems/Problem 22"
5849206328x (talk | contribs) (New page: ==Problem== The letters <math>\text{A}</math>, <math>\text{J}</math>, <math>\text{H}</math>, <math>\text{S}</math>, <math>\text{M}</math>, <math>\text{E}</math> and the digits <math>1</ma...) |
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The letters <math>\text{A}</math>, <math>\text{J}</math>, <math>\text{H}</math>, <math>\text{S}</math>, <math>\text{M}</math>, <math>\text{E}</math> and the digits <math>1</math>, <math>9</math>, <math>8</math>, <math>9</math> are "cycled" separately as follows and put together in a numbered list: | The letters <math>\text{A}</math>, <math>\text{J}</math>, <math>\text{H}</math>, <math>\text{S}</math>, <math>\text{M}</math>, <math>\text{E}</math> and the digits <math>1</math>, <math>9</math>, <math>8</math>, <math>9</math> are "cycled" separately as follows and put together in a numbered list: | ||
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<cmath>\begin{tabular}[t]{lccc} | <cmath>\begin{tabular}[t]{lccc} | ||
& & AJHSME & 1989 \\ | & & AJHSME & 1989 \\ |
Latest revision as of 16:03, 19 April 2021
Problem
The letters , , , , , and the digits , , , are "cycled" separately as follows and put together in a numbered list:
What is the number of the line on which will appear for the first time?
Solution
Every line has as part of it and every line has as part of it. In order for both to be part of line , must be a multiple of and , the least of which is .
See Also
1989 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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 AJHSME/AMC 8 Problems and Solutions |