Question 8
A sidewalk has integer length $1\le N\le1000$. Lay Fibonacci-length tiles 1,1,2,3,5,8,… in increasing order starting at the first 1. When the next tile exceeds the uncovered remainder, restart at the first 1. Each start or restart is a new sequence. Choose the smallest N that requires the greatest number of sequences. How many tiles are used altogether? For example N = 26 uses 11 tiles in three sequences: (1,1,2,3,5,8), (1,1,2), (1,1).
