Addendum

Manuel R. Pablo, of the Naval Research Laboratory, Washington, D.C., surprised me by finding another solution to the old T puzzle. By turning one piece over he produced the fat T shown in Figure 80. Other readers, keeping the five-sided piece in its standard orientation, produced '/'s with arms of different lengths.

Pablo's solution to the T-puzzle

Note that if one piece is turned over, the four pieces fit neatly together to form the isosceles trapezoid shown in Figure 81. The T puzzle, packed in this trapezoidal form, was on sale in 1975 as the "Teezer" puzzle, made by Hoi Polloi, New York City.

The T puzzle has been made with the T in many different shapes, but the puzzle is difficult only if the five-sided piece has the same width as the others. The mind has a strong tendency to assume that this piece must go either vertically or horizontally, an assumption that of course makes the solution impossible.

David Frost was so intrigued by the leprechaun paradox that he arranged for Pat Patterson to provide an enlargement that he could display on the TV talk show he was then hosting. After demonstrating the paradox, Frost asked if anyone in the audience could explain it. Nobody could. Finally a lady stood up to say that her husband understood how it worked. Frost turned to the husband. His explanation was identical with the one I quoted for Loyd's vanishing Chinese warrior. When the rectangles are arranged one way, the man said, there are 15 leprechauns. But when you arrange them the other way, there are only 14.

Figure 81

Figure 81

The "Teezer" puzzle

In showing the paradox to friends, an amusing bit of business is to ask which leprechaun vanishes. If they pick one, put a penny on the upper half and another penny on the lower half. After shifting the pieces, the pennies of course mark portions of leprechauns that are still there. Let them try again. The number of pennies on the figures increase, but without casting much light on the mystery.

Many readers wrote to say that if the lower half of the picture is cut in two parts by a vertical cut between the ninth and tenth leprechauns, you can arrange the four pieces to make 13 leprechauns. Other permutations produced by other cuts will give 16 and 17 figures, though they get distorted as they increase. Of course you can produce similar changes by rotating Loyd's disk.

Dozens of imitations and variations of the leprechauns have been printed since the item was first marketed, some of them pornographic. You will find an early discussion of how they all work, with many examples, in my Mathematics, Magic and Mystery, and in Mel Stover's cover article, "The Disappearing Man and Other Vanishing Paradoxes," listed in the bibliography. Stover owns the largest collection of such things, mine running a close second.

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