Difference between revisions of "1990 AJHSME Problems/Problem 19"
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<math>p</math> is a person seated, <math>o</math> is an empty seat | <math>p</math> is a person seated, <math>o</math> is an empty seat | ||
| − | The pattern of seating that results in the fewest occupied seats is | + | The pattern of seating that results in the fewest occupied seats is <math>o<cmath>p</cmath>o<cmath>o</cmath>p<cmath>o</cmath>o<cmath>p</cmath>o</math><math>o</math>...<math>p</math><math>o</math> |
we can group the seats in 3s | we can group the seats in 3s | ||
| − | + | <math>o<cmath>p</cmath>o</math> <cmath>o</cmath>p<math></math>o<math> </math>o<cmath>p</cmath>o<math> ...</math>o<cmath>p</cmath>o<math> | |
| − | there are a total of <math>\boxed{B} | + | there are a total of </math>\boxed{B}$ groups |
==See Also== | ==See Also== | ||
Revision as of 07:20, 15 November 2019
Problem
There are 
seats in a row. What is the fewest number of seats that must be occupied so the next person to be seated must sit next to someone?
Solution
is a person seated, 
is an empty seat
The pattern of seating that results in the fewest occupied seats is 
...
we can group the seats in 3s
![\[o\]](http://latex.artofproblemsolving.com/d/0/a/d0a14010d80c69d4d7711409b864f44e3d59ae5b.png)
p$$ (Error compiling LaTeX. Unknown error_msg)o$$ (Error compiling LaTeX. Unknown error_msg)o![\[p\]](http://latex.artofproblemsolving.com/8/a/5/8a53d232841e40077f875ae3c271284d48e36a09.png)
o
oo
\boxed{B}$ groups
See Also
| 1990 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 18 |
Followed by Problem 20 | |
| 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 | ||
