Question 105
One cuts a paper strip of length $2007$ into two parts of integer lengths and writes down the two integers on the board. Then cuts one of the two parts into two parts of integer lengths and writes down the two integers on the board. The cutting stops when all parts are of length $1$. A cut is called *bad* if the two parts obtained are not of equal lengths.
a) Find the minimum possible bad cuts.
b) Prove that for all cuttings with minimum possible bad cuts the number of distinct integers on the board is one and the same.
a) Find the minimum possible bad cuts.
b) Prove that for all cuttings with minimum possible bad cuts the number of distinct integers on the board is one and the same.