Tangram Paradoxes – Explaining the Phenomenon

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The tangram is a Chinese puzzle which is similar to the Western jigsaw puzzle, but differs from the same in always having seven pieces, which are fitted together in numerous ways to make an almost infinite number of different shapes. One of the oddities and perhaps the single most intriguing thing about the tangram is the phenomenon on Paradoxes.

Paradox shapes are two puzzle configurations which are almost the same, with one super-interesting quirk: a portion or portions in one “magically” disappears on the other version. The Dudeney paradox of two monks is the most common example: where on one version, the silhouette figure is a complete person; and on the second version, the figure loses its foot.

Given side-by-side illustrations of these puzzles, many actually begin to believe the “vanishing” proposition. But how can it be possible for a portion to disappear, when the same exact seven pieces are always being used to solve each puzzle? What is really going on here?

In order for all not to be lead astray, always reconcile that the total surface area of the tans (puzzle pieces) always remain constant. In other words, if portions begin to disappear, all you need to look for is where areas are shifted–or transferred to. In this way, you will begin to understand that on the Dudeney monk paradox, the area of the foot that disappears, is actually shifted to the body of the monk. Closer inspection will reveal that between the two puzzle versions, the monk’s body does not actually remain constant.

The sleight of hand actually lies in the pre-presentation of these Paradoxes. When the presenter approaches you with, “Can you believe this? The foot of the monk disappears in the other version!” Then proceeds to show you the side-by-side figure-drawing, then demonstrates the puzzle with actual tangram pieces…

There are numerous other tangram paradoxes. Such as: a flatiron that loses its knob, many vases which lose some portion of it or gain a hole on a portion of it, a wrench that loses its base, and others. With the above explanation in place, we should now look at paradoxes differently; no longer believing that portions actually disappear. Instead, we now watch out–where the areas are shifted.

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