Twisted rope Imagine a length of rope whose cross section is a regular polygon. You join the ends together with a powerful glue, but before doing so you give one end a twist so that faces are matched up with different faces. Now color each face a different color. How many colors are needed to color ...

Wall king A king likes to walk. He instructs his gardener to plant hedges to build a spiral in which he can walk. The gardener starts with three sides of a square, each 100 of the king's paces long. On the fourth side of the square, he plants a hedge only 98 paces long. He then plants another 98-pac...

Spaghetti holes I want to make one of those measuring tools for spaghetti. It s a board with holes of various sizes in it. There s a hole through which you stick enough spaghetti to feed 2 people, another hole for 3 servings, another for 4. I know that the hole for 2 servings has a diamter of 1 inch...

Solving an equation Solve the equation 6x + 2 = 16 in as many ways as you can. Approaches What's a solution? response: remind of earlier definition: a number you substitute for x to get a true statement. For example, is 2 a solution? Guess and check. There's no solution. response: Why not? Are there...

Potent problems. . . . . . are problems that have the potential to deepen understanding of significant mathematics through multiple answers approaches to an answer interpretations extensions perspectives on a mathematical idea layers of complexity algorithms Problems with multiple solutions and/or m...