1990 AJHSME Problems/Problem 19: Difference between revisions

Revision as of 07:22, 15 November 2019

There are $120$ 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?

$\text{(A)}\ 30 \qquad \text{(B)}\ 40 \qquad \text{(C)}\ 41 \qquad \text{(D)}\ 60 \qquad \text{(E)}\ 119$

$p$ is a person seated, $o$ is an empty seat

The pattern of seating that results in the fewest occupied seats is opoopoopoo...po we can group the seats in 3s opo opo opo ... opo

there are a total of $\boxed{B}$ groups

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

@@ Line 9: / Line 9: @@
 <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 <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>
+The pattern of seating that results in the fewest occupied seats is opoopoopoo...po
 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>
+opo opo opo ... opo
-there are a total of </math>\boxed{B}$ groups
+there are a total of <math>\boxed{B}</math> groups
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