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rocdocmac

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Posts posted by rocdocmac


  1. On 2017/05/12 at 0:25 PM, rocdocmac said:

    Use the twelve pieces on the left to create a chess board, The pieces may be flipped!

    CB Puzzle.jpg

     

    CB Puzzle.jpg

    On 2017/05/12 at 0:25 PM, rocdocmac said:

    Use the twelve pieces on the left to create a chess board, The pieces may be flipped!

    CB Puzzle.jpg

     


  2. Spoiler

    I've done this exercise before (round about 2005), working through each and every possible move, which naturally took a long time. I saw my solution that I printed out at that time about three months ago, but now I can't find it anywhere! I'm almost certain that the mouse's path went through all 27 cubes, but so far I couldn't replicate that! Till I find that printed solution again, we'll have to accept 25 as the maximum and Thalia was indeed the winner. So, apology for the "have another go"!. Incidentally, if the center is omitted, you still get 25 of the 26 remaining cubes.

     

     

    No center.jpg


  3. Spoiler

    You'll get 25 if you start with the middle of an edge. Remember, however, there are 8 corners plus 6 faces (total 14), but 12 corners and a single center (total 13). Thus, to obtain the maximum one has to start at a corner or middle of a face and end with a corner or middle of a face.

    59196d08aab5f_BW.jpg.e8a31f0c65aee25aac5b81a7b046be92.jpg


  4. Hopefully this one has not appeared before...

    Suppose 27 identical cubical chunks of cheese are piled together to form a cubical stack, as illustrated below. What is the maximum number of these cheese chunks through which a mouse of negligible size could munch before exiting the stack, assuming that the mouse always travels along the grid of 27 straight lines that pass through the centers of the chunks parallel or perpendicular to their sides, always makes a 90 degree turn at the center of each chunk it enters, and never enters any chunk more than once?

    Figures.jpg

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