Lewis Carroll Puzzles

Here is Lewis Carroll's Jabberwocky.

For more Lewis Carroll puzzles, check out "Lewis Carroll's Games and Puzzles" and "Rediscovered Lewis Carroll Puzzles" edited by Edward Wakeling and published by Dover Publications, Inc.

1. Draw the figure shown without lifting your pencil from the paper, without retracing any edge and without crossing your own path. How many such paths are possible?
   
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2. Move exactly four of the cakes shown to make five rows with four cakes in each row.
   
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3. A clock has hour and minute hands of the same length and no numerals on its face. At what time between 6 and 7 o'clock will the time on the clock appear to be the same as the time read on the reflection of the clock in a mirror?
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4. You are given two glasses. One contains 50 tablespoons of milk, the other 50 tablespoons of water. Take one tablespoon of milk and mix it with the water. Now take one tablespoon of the water/milk mixture and mix it with the pure milk to obtain a milk/water mixture. Is there more water in the milk/water mixture or more milk in the water/milk mixture?
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5. If you paint the faces of a cube with six different colors, how many ways are there to do this if each face is painted a different color and two colorings of the cube are considered equivalent if you can rotate one to get the other? What if we drop the restriction that the faces be painted different colors?
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6. Find three right triangles with sides of integer length all having the same area.
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7. DOUBLET: Make a "word ladder" from FOUR to FIVE. Every step in a word ladder differs from the previous step in exactly one letter and each step in the ladder is an English word.
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8. RIDDLE: Why is a raven like a writing desk?
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Please send any questions or comments to: lesreid@math.missouristate.edu

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