The Riddle of the Tiled Hearth is one of many mathematical puzzles from Henry Ernest Dudeney's 1907 book titled The Canterbury Puzzles And Other Curious Problems. The first group of puzzles in this book are based on the characters from Geoffrey Chaucer's Canterbury Tales. Puzzles from this book could be used as part of a cross curricular unit on history, literature and mathematics. There are a number of very interesting puzzles and games including the first pentomino puzzle called The Broken Chessboard and a clever variation of the game Nim called The Thirty One Game. Since this book was first published in 1907, the copyright has expired and it is freely available on Project Gutenberg. It seems that it was Friar Andrew who first managed to "rede the riddle of the Tiled Hearth." Yet it was a simple enough little puzzle. The square hearth, where they burnt their Yule logs and round which they had such merry carousings, was floored with sixteen large ornamental tiles. When these became cracked and burnt with the heat of the great fire, it was decided to put down new tiles, which had to be selected from four different patterns (the Cross, the Fleurdelys, the Lion, and the Star); but plain tiles were also available. The Abbot proposed that they should be laid as shown in our sketch, without any plain tiles at all; but Brother Richard broke in, To use this activity with students, I would start by introducing using the tiled hearth story as written above. Then I would introduce some manipulatives that would let them physically explore and work with the puzzle. I would give each group of students a large 4x4 grid on a sheet of paper and some multilink cubes of 4 different colours.
One aspect of this puzzle that I like is that students can play around with it and have some intermediate success. They might just place a few cubes on the grid. With time, they can refine their solutions to get better and better. Below shows how a student might explore to place more and more cubes. The Solution from Canterbury Puzzles shows that the best solution leaves 3 blank spaces. Dudeney states, "The correct answer is shown in the illustration on page 196. No tile is in line (either horizontally, vertically, or diagonally) with another tile of the same design, and only three plain tiles are used. If after placing the four lions you fall into the error of placing four other tiles of another pattern, instead of only three, you will be left with four places that must be occupied by plain tiles. The secret consists in placing four of one kind and only three of each of the others." Below are both my solution using cubes and Dudeney's equivalent solution. EL
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