Further Questions about Tetrads
8. Why was the order-11 polyomino tetrad not found earlier?

According to a letter from Martin Gardner dated January 10th 1980, I was then the only reader who had found a tetrad made of four congruent order-11 polyominoes (see question 9). That's easy to explain. Unlike me, most Scientific American readers are intelligent people. And intelligent people do not waste time. Before tetrads were published in Scientific American dedicated puzzle solvers had more than one year to search for an order-11 polyomino tetrad. In those days it seemed to be very unlikely that such an object could exist, and searching for 'non-existing' objects would have been really wasting time.

The following is speculative because I do not remember how I found the order-11 polyomino tetrad.

Step 1
Start with a well-known tetrad made of order-12 polyominoes.

Step 2
Reduce the lengths of the polyominoes. Only the connection of the blue and green polyomino is missing.

Step 3
Add a cell on the left side of the green polyomino. Then such a cell has also to be added to the yellow polyomino. Therefore move the green polyomino one step downwards.

Step 4
But now the connection of the red and green polyomino is missing. Try the following.

Step 5
The other polyominoes get the same shape as the red one. The blue polyomino has to move one step to the left.

Step 6
Four small holes occur. They can be filled by moving the blue and the green polyomino one step downward and additionally the green polyomino one step to the left.

Step 7
Now it is possible to add two cells to each polyomino without cutting off any cell.

The importance of this tetrad was much higher in 1979 than it has become today. At that time, only a few people could make use of a computer.

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 Walter Trump, Nürnberg, Germany, ms(at)trump.de, © 2020-02-12 (last modified: 2020-02-12)