Tangram Paradox Explained

Tangrams, one of SiamMandalay's favorite puzzles and all time classic. Basically, Tangram's are a 7-piece puzzle that originated from China, they are similar to a western version of the jigsaw puzzle. Ever green in popularity, they have been in the Western world for over 200 years.

One of the oddities and perhaps the most intriguing part of the Tangram is the phenomenon of Paradoxes.

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Firstly: What is a paradox puzzle? Tangram paradoxes are designs that can be built with all the 7 pieces of the game and appear to identical in mass but have slightly differing configurations. The eye catching quirk is that a portion of one “magically” disappears on the other.

The Dudeney Paradox of two monks (above) is the most famous and common example, where it appears that one monk is complete and the other is missing a foot.

When viewed side-by-side, many people actually begin to believe the “Vanishing” proposition – how is this possible? What is really going on? In actuality the Dudeney Paradox is probably not the most subtle in terms of difference, you can clearly see under close observation that one monk is marginally shorter than other. Other paradoxes are little bit harder to spot.

In order to not be fooled you must recognize that the surface area of the pieces always remains constant (I’m sorry, there is no super-duper magic).

To figure out where the space has gone you just need to look where areas have been transferred or shifted to and from. Once you have realized this, you will see that the monks are not actually identical. Everything has been moved slightly. This is the same for all paradoxes, the one below – is a lot more subtle.

Here, although all pieces have been used the paradox is slightly longer, it’s hard to compare as they are identical in height.

The sleight of hand that achieves this effect is by presenting these puzzles side by side, they appear to have the same height however, their width is marginally different enough all the way around that in the end you can be missing a significant portion of the puzzle.