You have to cut a stick 100 units long into 100 pieces Find

You have to cut a stick 100 units long into 100 pieces. Find the minimum number of cuts required if you are allowed to cut several stick pieces at the same time.

Solution

The sticks can be cut into pieces with one stick being cut into half. Since you are allowed to cut several stick pieces at the same time, the number of cuts will be minimised only when the cut pieces are grouped together to produce another cut.

For instance, the first cut will produce 2 sticks of 50 units each (If it is cut along the middle). These two units can be grouped together on above the other and another cut can be made. This will give four sticks of 25 units each. Again this can be grouped together and cut to give 8 sticks of 12.5 units each.

This will go on:

Out of the 64 pieces, (100-64=36) pieces of length 1.5625 units are taken, clubbed and cut. This will produce (36x2=72) sticks of length 0.78125 units and we will be left with (64-36= 28 units) of length 1.5625 units.

Thus we will have 100 pieces of the inital stick with the following dimensions:
72 pieces of length 0.78125 units and 28 pieces of length 1.5625 units. Since there is no restriction on the final length of the pieces, this is the optimal solution