Loading...
ISEE Upper Level
Quantitative Reasoning

Seating Arrangements Challenge

Very Hard Word Problems Advanced Algebra

Ami and Ravi are planning to distribute seats in a theater for an upcoming play. The theater has rows with a seating arrangement of 10 seats each. The two friends decide to allocate seats in such a way that:

1. If Ami takes 3 consecutive seats in any row, Ravi will take 4 consecutive seats in the same row but must leave at least 1 seat empty next to any block of Ami’s seats.

2. If Ami chooses non-consecutive seating of 2 seats, Ravi can take up to 5 consecutive seats in that row, again leaving at least 1 empty seat next to Ami's choice.

Given that there are 10 rows in total, how many unique seating arrangements can be made in one of the rows if Ami chooses to take 2 consecutive seats?

Hint

Submitted10.0K
Correct9.0K
% Correct90%