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Math Help - Doublets

  1. #1
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    Doublets

    Doublets is a game which was invented by Lewis Carroll, who described it in these words: 'Two words are proposed, of the same length; and the puzzle consists in linking these together by interposing other words, each of which shall differ from the next word in one letter only. . . . As an example, the word 'head' may be changed into 'tail' by interposing the words 'heal, teal, tell, tall.' Thus Carroll changed 'head' into 'tail' in five moves:

    HEAD
    HEAL
    TEAL
    TELL
    TALL
    TAIL

    Try to make the following transformations in the specified number of moves.

    1. Change CAT into DOG in three moves.

    2. Change BOY into MAN in three moves.

    3. Change HARD into EASY in five moves.

    4. Change EAST into WEST in three moves.

    5. Change ONE into TWO in eight moves.

    6. Change BREAD into TOAST in seven moves.

    7. Change SICK into WELL in four moves.

    8. Change RICH into POOR in six moves.

    9. Change GRASS into GREEN in seven moves.

    10. Change TREE into WOOD in eight moves.

    11. Change HATE into LOVE in three moves.

    12. Change BLACK into WHITE in seven moves.
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  2. #2
    Moo
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    1. Change CAT into DOG in three moves.
    Spoiler:
    CAT > COT > DOT > DOG


    2. Change BOY into MAN in three moves.
    Spoiler:
    BOY > BAY > MAY > MAN


    4. Change EAST into WEST in three moves.
    Spoiler:
    EAST > VAST > VEST > WEST


    11. Change HATE into LOVE in three moves.
    Are participles allowed ?
    Spoiler:
    HATE > HAVE > HOVE > LOVE
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  3. #3
    MHF Contributor
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    This type of problem was talked about in a very interesting book, Prime Obsession by John Derbyshire. He made some interesting theorems about this type of problem.
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