Arrange a deck of cards in alternating colors, black and red. Now cut the deck so that the bottom card of one pile is black and the other is red. Riffle-shuffle the two piles together again. Now remove cards from the top of the pack in pairs. How many of these pairs should we expect to contain cards of differing colors?

Surprisingly, all of them will. During the shuffle, suppose a black card falls first. It must be followed by either the next card in its own pile, which is red, or the first card from the other pile, which is also red. Either way, this first pair will contain one black card and one red card, and by the same principle so will each of the other 25 pairs produced by the shuffle. This effect was first identified by mathematician Norman Gilbreath in 1958.

Related: Arrange the deck in a repeating cycle of suits, such as spade-heart-club-diamond, spade-heart-club-diamond, etc. Ranks don’t matter. Now deal about half of this deck onto the table and riffle-shuffle the two halves back together. If you draw cards from the top in groups of four, you’ll find that each quartet contains one card of each suit.

See So Much for Entropy.

A calendar curiosity by Canadian magician Mel Stover:

Offer any month’s calendar to a friend and have him outline a 4×4 square of dates. Ask him to circle any date in that square and cross out the other numbers in its row and column. Have him do this three more times and then add the circled numbers.

You can predict his answer by totaling the numbers in either pair of diagonally opposite corners in the square and doubling that number. Why does this work?

From Royal V. Heath, Scripta Mathematica, June 1952:

In the square above, all rows, columns, and diagonals produce the same sum. And:

16 + 11 + 13 + 10 = 9 + 14 + 12 + 15
16 + 17 + 14 + 3 = 11 + 22 + 9 + 8
2 + 15 + 20 + 13 = 5 + 12 + 23 + 10
16 + 5 + 17 + 12 = 20 + 9 + 13 + 8
2 + 11 + 15 + 22 = 14 + 23 + 3 + 10
10 + 16 + 17 + 23 = 11 + 13 + 20 + 22
2 + 8 + 9 + 15 + 11 + 13 + 20 + 22 = 3 + 5 + 12 + 14 + 10 + 16 + 17 + 23

Most remarkably, everything above holds true if you square each term.

In studying metabolism in the early 1600s, Santorio Santorio undertook a unique study: He conducted his daily activities on a platform attached to a steelyard scale. After years of readings, he learned that his food always weighed more than his excretions, and concluded that the rest was lost through “invisible perspiration,” the loss of matter through the pores and breath.

Santorio’s conclusions remained the state of the art for more than a century. When Ben Franklin wrote in 1742, “If thou art dull and heavy after Meat it is a sign that thou hast exceeded due measure,” he was essentially repeating Santorio’s aphorism of 150 years earlier, “Meats which promote Perspiration bring Joy, but those which obstruct it Sorrow.”

How to clean a 40-foot spectrograph, from R.W. Wood’s Researches in Physical Optics, 1913:

“The long tube was made by nailing eight-inch boards together, and was painted black on the inside. Some trouble was given by spiders, which built their webs at intervals along the tube, a difficulty which I surmounted by sending our pussy-cat through it, subsequently destroying the spiders with poisonous fumes.”

This was the least of Wood’s exploits. Walter Bruno Gratzer, in Eurekas and Euphorias, writes that the physicist “would alarm the citizens of Baltimore by spitting into puddles on wet days, while surreptitiously dropping in a lump of metallic sodium, which would explode in a jet of yellow flame.”

The north pole is the south pole. Earth’s north magnetic pole is actually the south pole of its magnetic field — a compass needle points “north” because opposites attract.

(Thanks, Jeremy.)