“Isn’t the rest of the board the sixth piece?” demanded the carpenter.
The students looked rather blankly at each other; and Mr. Brookbine saw that they were not convinced, simple as the problem was.
He took a stick, and cut it so that it was twenty-four inches long. Using his rule, he marked it off into pieces four inches in length. Sawing off the piece on the right of the first mark, he handed it to Steve. He asked the students to count as he cut off the lengths.
“Five!” screamed the boys when he had made the fifth cut.
“Here is the sixth piece. It is just four inches long. Now, where shall I put in the sixth cut?” asked Mr. Brookbine, as he handed the rest of the stick to Steve. “You have six pieces, though I have cut but five times.”
“That’s so; but I can’t see why it should be so,” replied Steve vacantly.
“The first four cuts each gave me one piece, or four pieces in all. The fifth cut gave me two pieces, did it not? for the rest of the board is a piece as well as the others.”
All of them could see it then; and the principal
applied the result to other numbers, and the students were willing to admit that an equal division into ten parts was made with nine cuts.
“It is surprising how little things bother us sometimes,” continued Mr. Brookbine. “But we shall never get our shelves made at this rate. As we have leeway enough in the length of this board, we will cut the pieces four feet and one inch in length. Nat Long, you may measure it off on one side, and, Ned Bellows, you may do the same on the other side.”