This brainteaser was created by Julia Zurkovsky. When the ends of the rope below are pulled in opposite directions, how many knots will be formed along the rope’s length? Resources for Teaching Math
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http://illuminations.nctm.org
Solution: 0 knots. Look at each letter individually. The basic letters (like r, i, n, e and the two s’s) can be analyzed by inspection, and it can be seen that none of these letters will form a knot when the rope is pulled tight. There is a twist in each of the two a’s. When pulled tight, however, the twists will slip past each other and no knots will be formed. The B and t appear to be more complex than the other letters. The small loop at the top of the B will obviously not form a knot by itself. When the lower half of the B is unwrapped from the vertical stem (as shown below), it can be seen immediately that the rope will straighten out as both ends are pulled. Consequently, no knots will be formed by the B. The t consists of five unconnected loops. When the bottom left segment of the t is pulled as shown below, the upper left loop will be pulled through the middle loop, straighten and disappear. Once that loop is gone, the lower right segment can be pulled to straighten the upper right loop. The remainder of the rope will then yield no knots when pulled tight. Consequently, no knots will be formed along any portion of the rope when the ends are pulled. Resources for Teaching Math
© 2010 National Council of Teachers of Mathematics, Inc.
http://illuminations.nctm.org