(But they aren't.).Ĭut 6: at $2$ give him at most $64$ (actually $50$) pieces the largest of which is $2$ but one my be smller. ($1$ is shorter at $4$ inches).Ĭut 5: at $4$ gives him at most $32$ (actually $25$) pieces the largest of which is $4$ but one may be smaller. Peace is a noun used to describe the calmness of a situation or freedom from disturbance. Piece means to be a part of something bigger, a part of a whole, and can work as a noun or verb to describe something or put together multiple pieces. ($1$ is shorter at $4$ inches).Ĭut 4: at $8$ gives him at most $16$ (actually $12$) pieces the largest of which is $8$ but one may be smaller. Piece and peace are homophones: two words that sound identical despite their obvious differences. (one is shorter at $4$ inches)Ĭut 3: at $16$ gives him at most $8$ pieces (actually $6$) the largest of which is $16$ but one may be smaller. (one is $36$ inches)Ĭut 2: at $32$, give him at most $4$ pieces the largest of which are $32$ but one may smaller. You could reason he need $7$ cuts so he might as well always cut at the $2^k$ mark.Ĭut 1: at $64$, gives him at most $2$ pieces the largest of which are $64$ but one may be shorter. This isn't the only way to do it in $7$ but $7$ is required. piece together: phrasal verb to make (something) by bringing together various parts or pieces : to bring together (various parts or pieces) to form one complete thing. (he now has $2$ inch pieces ($44$) and some $1$ inch pieces ($12$).) (he now has some $4$ inch pieces ($16$), so $3$ inch pieces ($8$), some $2$ inch pieces ($4$), and some $1$ inch pieces ($4$). $4$ of each).įourth is at $7$ (he now has some $7$ inch pieces ($8$), some $6$ inch pieces ($4$), and some $5$ inch pieces ($4$).)įifth cut at $4$ inches. (he now has some $13$ inch pieces and some $12$ inch pieces. If first cut is at the $50$ (He now has $50$ inch pieces. $2^6 < 100 < 2^7$ so he needs at least $7$ cuts.īut if he cuts exactly in half his pieces will not be exactly $1$ inch. 2 female dresses and gold drops-sprays Tow pieces of kitenges 3 peices of. So in $n$ cuts he will have $2^n$ pieces. Ivory tusk 400 pieces white cloth, 6 pieces green 20 pieces white rools. If he stacks every piece and cuts everything in half he will double his pieces each cut. I believe that this algorithm of always cutting the largest power of two which is smaller than the largest piece will be optimal in general, not just for 100 pieces. Cut the pieces into 100 pieces of length 1.Cut the pieces into 50 pieces of length 2.Cut the pieces into 25 pieces of length 4.Cut the pieces into 12 pieces of length 8 and 1 piece of length 4.Cut the pieces into 6 pieces of length 16 and 1 piece of length 4 (in this step we do not actually cut the piece of length 4).In all future cuts we will also start by laying the pieces so that their left ends line up.
The cheese was cut into small pieces and arranged on a silver platter. Lay the pieces so that the left ends line up, and then cut so that you have 3 pieces of length 32 and 1 piece of length 4. a : an amount that is cut or separated from a larger section of something Divide the pie into six equal pieces.Cut the stick into a length of 64 inches and a length of 36 inches.Therefore, you will need to make at least 7 cuts (since $2^6 = 64 100$). First, each cut can at most double the number of pieces you have.
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