Panda square

Place the 16 tiles in the 4×4 square frame so that the colors of the sides being touched match.

  • Location:
  • Minimum age: from 6 years old.
  • Required time: 15 minutes.
  • Number of participants: One or more people
  • Keywords: Puzzle, symmetry, square
  • Taxonomy: Geometry, Combinatorics

Més reptes? Ajuda?

The 16 pieces

To build the pieces, the square is divided into 4 equal squares and painted black or white in all possible different shapes. Rotations that would make some equal pieces are not taken into account. 

The solutions

There are many possible solutions, so getting one is affordable. 

Normally, the process is to fill the frame with the pieces until it is detected that none of the remaining pieces can be put on, then it is time to reflect and reposition some sins. 

We encourage you to share your solution on social media with the hashtag #pandasquare

#pandasquare

Ivan Moscovich, the great initiator of interactive scientific museums

This puzzle appears under the name BITS in Ivan Moscovich's book "Super games"

Ivan Moscovich was born to Jewish parents in Vojvodina (now Serbia) in 1926. At the age of 17 he was interned in the Auschwitz concentration camp. He went through 4 concentration camps and 2 forced labor camps.

After the war he studied mechanical engineering at the University of Belgrade and emigrated to Israel where he worked as a scientific researcher involved in the design of teaching materials, educational aids and educational games.

In 1964 he founded the Tel Aviv Museum of Science and Technology. This was one of the museums that changed the traditional exhibition form, incorporating many interactive science, mathematics, and art materials. One of his visitors was the physicist Frank Oppenheimer, whose ideas, designs and materials were the seed of the revolutionary Exploratorium in San Francisco that Oppenheimer inaugurated in 1969 and which is still a benchmark for interactive museums like ours.

Ivan Moscovich at 93 years old. (source: jewishjournal.com)

Moscovich is a tireless writer, has more than 30 books on the Amazon website, all of them recommended, constitute an inexhaustible source of original ideas.

He is also a great creator of games such as the mythical "Magic robot", "Magic mirror", "Tricky fingers", "30cubed" or "Fold"

magic-robot-game
magic_mirror
trick finders
30cube
folded

Research on solutions

David Butler , professor at the Mathematics Learning Centre at the University of Adelaide (Australia), explains on his blog how in 2016 he took the idea out of Ivan Moscovich's book and named it PANDA SQUARE. 

It is interesting to list the questions it raises, some with answers, others that are still open:

  • Is any solution possible with some kind of symmetry or rotation?  What symmetries can be ruled out?
  • How many solutions are there?
  • From a solution, how many derivative solutions can be easily found?
  • Is it possible to have a solution where all identical tiles are in a different orientation?
  • Is there a solution with a single black region connected?
  • It seems that in the solutions found always at least one of the all-black or totally white tiles are at the edges. Can you try it?
  • Is it possible that the all-black tile is on one edge and on the opposite edge is the all-white tile?
magic_mirror

In 2020, David Butler made a thread explaining the discovery and demonstration of the only 4 symmetric solutions.