Mathematical & Logical Puzzles -Q6

21. The Knight’s Tour (1)

            Place a knight on a 6 by 6 chess board (i.e. an ordinary chess board which is 2 squares short each way).  The knight may be placed on any square.  The problem is to visit each square once and once only by taking ordinary knight’s chess moves.

22. The Knight’s Tour (2)

            

On an ordinary 8 by 8 chess board, a knight stands in the top left-hand corner square.  The problem is to visit each square once and once only using the knight’s chess move.

23. Alice In Wonderland

            “Oh, dear,” said Alice mournfully, “I wish I didn’t have to go into the Wabe, for that is where the Jub-Jub lives.”

            “Nonsense!”, exclaimed the Mad Hatter.  “It lives in a Tum-Tum tree.”  And addressing the March Hare, “Doesn’t it?”

            “Of course it does,” agreed the March Hare.  “Everybody knows that, don’t you agree?” (Here he prodded the Dormouse who was asleep on his shoulder).

            The Dormouse opened one sleepy eye and wearily muttered, “Yes, yes of course,” and promptly went back to sleep again.

            “Talking of birds,” said the March Hare, “the Bandersnatch is exceptionally shy this year.”

            “But I’m sure the Bandersnatch is an animal,” said Alice.

            “My, you are ignorant,” said the Mad Hatter, “of course it’s a bird.”

            The Dormouse, who appeared to be sleeping was consulted once more and he wearily announced, “I agree with Alice.”  Then he returned to snoring once again.

            “The Jabberwock,” announced the Mad Hatter, “is an interesting animal.  It has four wings and feeds on Borogoves.”

            “It has four wings,” agreed Alice, “but surely it feeds on Raths.”

            “Poppycock!” snorted the March Hare, disturbing the poor Dormouse, who woke up suddenly and appeared to be at least half-listening for a change.  “It has five wings and feeds on Toves.”

            “Five wings and feeds on Raths,” corrected the Dormouse, who found staying awake much too much effort, especially when no-one seemed to know what he was talking about.

            At this point in the proceedings, the Cheshire Cat appeared, sitting on the branch of a near-by Tum-Tum tree.  He grinned and informed them that of the four zoological facts that each had volunteered, two each were true and two each were false.  Whereupon he disappeared until only the grin remained, and this slowly faded, starting from the corners and ending in the middle.  Which still leaves the following unanswered:  Where does the Jub-Jub live?  What is a Bandersnatch?  And how many wings has a Jabberwock and what does it feed on?

24. The Spider And The Fly

            In a rectangular room 30 metres by 12 metres by 12 metres, a spider is in the middle of one end wall and one metre from the ceiling.

            A fly is in the middle of the opposite end wall and one metre from the floor.  It is too paralysed with fear to move.

            What is the shortest distance that the spider must crawl across the surfaces of the room in order to reach the fly?

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