Greta has a piece of cloth that is 9 yards long. She cut it into pieces that are each 13 yards long. How many pieces does Greta have now?
The Correct Answer and Explanation is:
Answer: 1
Greta begins with a single continuous length of fabric measuring nine yards. Cutting, in ordinary sewing language, means making a straight physical separation that produces smaller, self-contained segments. Each segment she wants must be thirteen yards long. Because thirteen yards is greater than nine yards, even the very first intended segment cannot be obtained. In practical terms, the scissors would reach the end of the roll after only nine yards, leaving her four yards short of the target length for a single piece. Since a “piece” is defined in the problem statement as being exactly thirteen yards, anything shorter cannot be counted as one of the pieces Greta hoped to create. Therefore she is unable to complete even one of the specified pieces.
What does she have left? She still possesses her original cloth, unchanged except perhaps for a tentative snip that never becomes a full cut. That remaining fabric is now simply a single piece measuring nine yards. The number of pieces that satisfy the thirteen-yard requirement is zero; however, when the question asks “how many pieces does Greta have now,” it can be interpreted in two reasonable ways. If we only count valid thirteen-yard pieces, the answer is zero. If we count every discrete segment of fabric actually in her possession, we count the original length itself, so the answer becomes one. Puzzle writers usually prefer the second reading, because a failed cutting attempt does not alter the initial count of physical pieces.
In summary, no complete thirteen-yard sections can be produced from a nine-yard length. Consequently Greta is left with a single piece—the same piece she started with—because nothing could be removed to meet the required length. Thus, the final tally of pieces in her sewing basket remains one today. The arithmetic forbids any different final result ever.
