Spud Loops

Given any pair of potatoes — even bizarre, Richard Nixon-shaped potatoes — it’s always possible to draw a loop on each so that the two loops are identical in three dimensions.

Do you see the simple, intuitive proof for this?

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Think of the potatoes as ghosts, and penetrate one with the other. The intersection of their surfaces forms the loop.

March 4, 2008January 16, 2013 | Puzzles · Science & Math

Q.E.D.

5 is one number.

2 and 3 are 5.

Therefore 2 and 3 are one number.

March 4, 2008 | Science & Math

Math Notes

175 = 1¹ + 7² + 5³

February 29, 2008 | Science & Math

The Three Cards Problem

I show you three cards. One is white on both sides, one is black on both sides, and one is white on one side and black on the other. I shake them in a hat, remove one at random, and place it on a table. The side that’s face up is black. What’s the probability that the other side is also black?

Hint: It’s not 1/2.

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The probability is 2/3 that the other side is also black. There are six faces. Of the three black faces, 2/3 are on the black/black card. So if you’re presented with a black face, chances are 2 in 3 that it’s on the black/black card — and thus that the card’s other side is black. See also Boy Trouble and The Monty Hall Problem.

February 27, 2008January 16, 2013 | Puzzles · Science & Math

“If the Indians Hadn’t Spent the $24”

In 1626 Peter Minuit, first governor of New Netherland, purchased Manhattan Island from the Indians for about $24. … Assume for simplicity a uniform rate of 7% from 1626 to the present, and suppose that the Indians had put their $24 at interest at that rate … and had added the interest to the principal yearly. What would be the amount now, after 280 years? 24 × (1.07)²⁸⁰ = more than 4,042,000,000. [The current value of Manhattan is] a little more than $4,898,400,000. … The Indians could have bought back most of the property now, with improvements; from which one might point the moral of saving money and putting it at interest!

— W.F. White, A Scrap-Book of Elementary Mathematics, 1908

February 24, 2008October 2, 2010 | History · Science & Math