Fibonacci's algorithm (exercise 9) is \greedy" in the sense that it chooses the least conceivable q at every step. A more complicated algorithm is known by which every fraction m/n with n odd can...

Fibonacci's algorithm (exercise 9) is \greedy" in the sense that it chooses the least conceivable q at every step. A more complicated algorithm is known by which every fraction m/n with n odd can be represented as a sum of distinct unit fractions 1/q₁
+ · · · + 1/q_k
with odd denominators. Does the greedy algorithm for such a representation always terminate?