1989 AJHSME Problems/Problem 22: Difference between revisions
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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: | ||
<cmath>\begin{tabular}[t]{lccc} | <cmath>\begin{tabular}[t]{lccc} | ||
& & AJHSME & 1989 \\ | & & AJHSME & 1989 \\ | ||
Latest revision as of 15:03, 19 April 2021
Problem
The letters 
, 
, 
, 
, 
, 
and the digits 
, 
, 
, are "cycled" separately as follows and put together in a numbered list:
![\[\begin{tabular}[t]{lccc} & & AJHSME & 1989 \\ & & & \\ 1. & & JHSMEA & 9891 \\ 2. & & HSMEAJ & 8919 \\ 3. & & SMEAJH & 9198 \\ & & ........ & \end{tabular}\]](http://latex.artofproblemsolving.com/7/1/1/7118a46dde66777eaf400e8ea2209dc386da0af5.png)
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 | ||
