So this level requires the player to decipher the rank 1 tensor, and then to use the information to put the Zoombinis in the hotel. In the game, the hotel is a rank 1 tensor. Just as a 2D tensor (a matrix) is rank 1 if all its information is given by two vectors: for some vectors and. Tensor flattenings are used in maths to give information about a tensor, often about its rank.Ī 3D tensor is rank 1 if all its information can be encoded by three vectors. We started with a 3D array of size 5 x 5 x 5, and made it into a 2D of size 25 x 5 by arranging the tree trunks side by side. In maths language: this hotel is a 5 x 5 x 5 tensor that has been flattened. Now the third direction “tree trunk” becomes a “depth” direction and we have a 3-dimensional 5 x 5 x 5 array. Imagine the five big tree trunks stacked one behind the other. Putting a Zoombini in the wrong room drops the Zoombini and damages that hotel room, and too many wrong tries will make the room off-limits. The player has to work out which are the three attributes that matter, and which of the three directions (row, column, tree trunk) they correspond to. the roller skaters all go in the third of the five columns) Regardless of which tree trunk they are on, Zoombinis with the same feet must go in the same columns of the tree trunk (e.g. Each tree trunk has five columns on it.Those with the same eyes go in the same tree trunk.Zoombinis with the same hair go in the same row of the hotel.The three attributes that matter are hair, eyes and feet.In Zoombinis language: three of the four attributes (hair, eyes, nose and feet) determine the right hotel room for the Zoombini. Here is a video of someone playing this level online, and below is a still from the video: The right room depends on the some of the features of the Zoombini. One of the stages of the game is called “Hotel Dimensia”, where you must find the right room for your Zoombinis in a hotel made of five tree trunks. The Zoombinis are created by the player in the first stage of the game:Įach Zoombini has four attributes, chosen from the table on the bottom left: hair, eyes, nose colour and feet. It lead us to wonder: what maths does Zoombinis actually involve? Coincidentally (or maybe not) Rachael and I both spent significant amounts of our childhood playing this game – just ask our siblings! We both strongly attribute our interest in logical puzzles and maths to this game. The aim of the game is to get your Zoombinis from Zoombini Isle to Zoombiniville via a series of logical puzzles. “The Logical Journey of Zoombinis” was a computer game first released in 1996.
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