Archived Stumpers (with solutions)
STUMPER #1.5: GOING IN CIRCLES
(Did you solve something differently? There's almost always more than one way to solve
a math problem. Sometimes there's even more than one correct solution!)
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1. How Did that Dot Get in There?
_Can you draw a circle with a dot in the center (as in the picture below) on a piece of paper? Here's the catch: you can use just one pencil and no erasing -- and cannot lift your pencil from the paper.
Draw a dot in the center of the paper. Fold the bottom corner of the paper up till it meets your dot. Draw a curve from the dot, along the folded section (which is really the back of your paper), until it goes off the fold and comes back on the front side of the paper a little distance away from the dot. Unfold the paper and continue drawing the circle. (One student suggested another solution: break your pencil in half and draw with two hands. Cheating, possibly, but a creative idea!)
2. In a Circle
_A number of children are standing in a circle. They are evenly spaced, and the eighth child is directly opposite the 18th. How many children are in the circle?
3. What Comes Next ?
_1024 chairs, numbered 1-1024, are arranged clockwise in a circle. Chair #1 is removed from the circle and chair #2 (the next chair, going clockwise) is left where it is. Continuing clockwise, the next chair is removed, and the one after it is left where it is. This continues until there is only one chair left in the circle. Which chair is it?
Too hard? Start smaller. What would be the last chair standing if there were 4 chairs? 8?
Too easy? What happens if there are an odd number of chairs? Start with 3 chairs and experiment with increasing odd numbers of chairs. See if you can discover any patterns.
Chair #1024 is the last one standing.