Chequered floor and Diamond palindrome

Chequered floor and Diamond palindrome

SOLVITUR AMBULANDO

On this chequered floor, paved with slabs each a foot square, the palindrome word ROTATOR can be traced in various ways.

If a man walks over it, taking one slab at every step, and never lengthening his strides, how many steps will he take in tracing every possible variation of the word, and how many such variations are there?

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|=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=|

+---+---+---+---+---+---+---+---+---+---+---+---+---+

| O |=R=| O | T | A | T | O | T | A | T | O |=R=| O |

+---+---+---+---+---+---+---+---+---+---+---+---+---+

| T | O |=R=| O | T | A | T | A | T | O |=R=| O | T |

+---+---+---+---+---+---+---+---+---+---+---+---+---+

| A | T | O |=R=| O | T | A | T | O |=R=| O | T | A |

+---+---+---+---+---+---+---+---+---+---+---+---+---+

| T | A | T | O |=R=| O | T | O |=R=| O | T | A | T |

+---+---+---+---+---+---+---+---+---+---+---+---+---+

| O | T | A | T | O |=R=| O |=R=| O | T | A | T | O |

+---+---+---+---+---+---+---+---+---+---+---+---+---+

|=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=|

+---+---+---+---+---+---+---+---+---+---+---+---+---+

| O | T | A | T | O |=R=| O |=R=| O | T | A | T | O |

+---+---+---+---+---+---+---+---+---+---+---+---+---+

| T | A | T | O |=R=| O | T | O |=R=| O | T | A | T |

+---+---+---+---+---+---+---+---+---+---+---+---+---+

| A | T | O |=R=| O | T | A | T | O |=R=| O | T | A |

+---+---+---+---+---+---+---+---+---+---+---+---+---+

| T | O |=R=| O | T | A | T | A | T | O |=R=| O | T |

+---+---+---+---+---+---+---+---+---+---+---+---+---+

| O |=R=| O | T | A | T | O | T | A | T | O |=R=| O |

+---+---+---+---+---+---+---+---+---+---+---+---+---+

|=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=|

+---+---+---+---+---+---+---+---+---+---+---+---+---+

A DIAMOND PALINDROME

Within the four corners of this Mystic Diamond the Palindrome, NAME NO ONE MAN, can be traced in 16,376 different directions, in straight lines, or at right angles, starting from the centre or from the borders.

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A. Cyril Pearson, TwentiethCentury Standard Puzzle Book, George Routledge & Sons, London, 1907.

Photo: pngwing

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