HOMEWORK 1
DUE: FEBRUARY 2, 2016
(1) [1, 2.1.27] Martha said: “I have been alive for all or part of five decades.” Rounded to the
nearest year, what is the youngest she could be?
(2) [1, 2.1.27] At my favorite library, if you select a book at random there is a 90% chance that
it has illustrations. Of all the illustrations in all the books, if you select one at random,
there is a 90% chance that it is in color. If the library has 10,000 books, then what is the
minimum number of books that must contain colored illustrations.
(3) [1, 2.1.27] A square can be cut into two congruent (i.e. same shape) polygons (by cutting it
in half) and can be but into four congruent polygons (by cutting along the two diagonals).
For which positive whole numbers n, can a square be cut into n congruent polygons.
(4) [2, 1] Below are the tire tracks left by the front and back wheels of a bicycle. Which way
did the bicycle go (left to right or right to left)?
(5) A king has 1000 bottles of wine, but a reliable source has told him that one of the bottles
has been poisoned. What is the fewest number of taste testers needed to figure out exactly
which bottle is poisoned. Suppose that the king needs to know before the party this evening
and that the poison is slow acting thus all the taste testers must do the tasting all at once.
Hint: The number is much smaller than you might initially think!
References
[1] Paul Zeitz. The art and craft of problem solving. John Wiley & Sons, 1999.
[2] Joseph D. E. Konhauser, Daniel J. Velleman, and Stan Wagon. Which way did the bicycle go?: and other
intriguing mathematical mysteries. Mathematical Association of America, 1996.
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