Make two lists; one consists of all powers of 10 in base 2, and the other all powers of 10...
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Making Magic Squares
A magic square is an NxN matrix in which every row, column, and diagonal add up to the same number....
Continue reading...Euler Characteristic
Take out a sheet of paper. Pop quiz! (just kidding). Draw any number of dots on your page. Now connect...
Continue reading...Matching Problem
Suppose I return N homeworks randomly to my N students. What is the chance that no student gets back her...
Continue reading...Toggling Light Switches
Imagine 100 light bulbs with light switches numbered 1 through 100, all in a row, all off. Suppose you do...
Continue reading...Suspended Rope Trick
What is the shape of a suspended rope? Is there some function that describes it? Answer: it’s the cosh curve!...
Continue reading...Calculus Limerick
Here’s a calculus limerick: Integral z-squared dz from 1 to the cube root of 3 times the cosine of three pi over 9 equals...
Continue reading...Why an International Date Line?
Can you find a continuous one-to-one function from the circle to the real line? Put it another way: is it possible, for...
Continue reading...Sums of Reciprocal Powers
You have seen that the harmonic series diverges. What about the sum of reciprocal squares? In fact, they converge, and to something...
Continue reading...Pizza Slices
Take a pizza and pick an arbitrary point in it. Suppose you cut the pizza into 8 slices by cutting...
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