It’s really rather counterintuitive, I think: when two screws are twiddled past each other, do they move closer, or move further apart, or stay the same distance from one another?

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This puzzle comes from the collected works of the great puzzler Sam Loyd:

How many eggs can be packed in a 6×6 crate, if no more than two can lie on any row, column, or diagonal (even a short diagonal), and an egg must be placed in each of two opposite corners?

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Help the poor paranoid scientists!

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A quite elementary question:

Imagine a tight band wrapped around the Earth (a perfectly spherical Earth!). If one foot is added to the band, it will be possible to lift it uniformly up, away from the surface of the Earth. Will the resulting gap be enough to pass a baseball card under? A baseball? A baseball player? 

Another variation, which is really quite amazing, is what if a foot is added and the band is lifted up in just one spot? How high will the band lift up? Higher than a seball? A baseball player? A baseball stadium?

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Another nice standard; it seems there is not enough information to solve this puzzle but it has a simple solution.

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This is a beautiful puzzle that appears in many different forms.

Arp and Bif are playing with a line of 100 flowers. Each flower is originally open. When an open flower is touched it closes, and when a closed flower is touched, it opens. First they touch every flower in the line, then they touch every other flower in the line, then they touch every third flower, etc. 

When done, which flowers are open, which flowers are closed?

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Edmund Harriss, sometime contributor to the Math Factor, makes his first appearance in this early segment, from February 29, 2004.

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How many ways can the astronauts link up to the space station?

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We ask: What do Google, flutes and monopoly have in common? In fact, important principles behind this question apply to an astounding array of phenomena!

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(Since we’ve been offline for a week or so, due to a tremendous ice storm that has paralyzed the town, we add a special bonus: the very first Math Factor episode ever aired, from January 25, 2004.)

Given a difference table, as we considered back in EV. What’s the Difference , how do we come up with a polynomial that gives the values on the top row?

For example, suppose we have

-1     -1     3     35     143     399     899 . . . . .
      0     4     32    108     256     500  . . . . .
         4    28    76     148      244  . . . . .
             24    48     72       96   . . . . .
                  24     24    24    . . . . .

What is the polynomial P(n), of degree four, that gives

P(0) = -1 P(1) = -1 P(2) = 3 P(3) = 35 P(4) = 143 , etc.

Can this be expressed simply in terms of the leading values on the left of the table: -1, 0, 4, 24, 24?

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