Track / Stage 4 / 332 of 340 #592 of 2000

Problem 592

AMC 12 late, AIME early

Combinatorics Difficulty 5.0 Find the answer

Variant 8.7.2. How many ways are there to arrange in a row $n$ crosses and 14 zeros so that among any three consecutive symbols there is at least one zero, if

(a) (2 points) $n=29$ ;

(b) (2 points) $n=28$ ?

Your answer

Official solution

Answer: (a) 15. (b) 120.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.