Entertaining Mathematical Puzzles

I have been intrigued by riddles recently and was actually looking for a riddle book, but all I could find were those stupid "Lateral Thinking" puzzles which I find completely worthless. So I found "Entertaining Mathematical Puzzles" by Martin Gardner, choosing it above other books mostly because it looked straight out of the 1960s, which reminded me of the types of books that entertained me when I was younger and visited my grandparents' houses. The book turned out to be awesome because it required no prior math knowledge, which made me wish that I had read this book as a sixth-grader or something.

Kids from my parents' generation were much more inventive with their modes of entertainment. They played so many games with pennies and toothpicks, which made the games more conceptual than fantastic--puzzles that are just asking for a mathematical interpretation. Video games aside, sudoku and crosswords today are so ubiquitous that I have always found "puzzles" to be a bit arbitrary. The interest in puzzles these days is comparable to someone who claims to enjoy chocolate but eats only Hershey's. There are so many interesting puzzles out there that are much more stimulating and rewarding!

Anyway, as a fledgling puzzler, my first realization was that a pleasure in solving puzzles is cultivated necessarily by really committing to discovering the solutions for yourself. Though this may seem obvious to you, before this book I usually read a puzzle, thought about it a minute or so, and if I didn't have the answer by then (or if I was close but didn't have the details down exactly) I would just flip to the book and say "Oh!" and move on. But this book helped me realize that puzzles, as with mathematics, are incredibly immersive once you dedicate yourself to the problem.

Here are some of my favorite problems from the book (answers not provided...you can do it!):

1. You are at the hardware store, and you notice that 1 costs 50 cents, 12 costs $1.00, and 144 costs $1.50. What is it that you are shopping for? [this is my all-time favorite puzzle]


2. A chemist is doing some experiments to see how his clothing affects his results. He finds that when he wears a green tie the experiment completes in eighty minutes, while if he wears a purple tie it takes one hour and twenty minutes. Why is this? 


3. Which two positive integers (not fractions), when multiplied together, make 13?


4. 8-5-4-9-1-7-6-3-2-0. How have these numbers been arranged? 


5. Can you draw the figure A in three strokes, where each stroke may not be interrupted by lifting your pen? If not, why? 


6. In a game for two players, there is a circle made of ten pennies (figure B). The players alternate turns, and each turn consists of the player removing either one penny of his choice or two adjacent pennies (no gaps or other pennies between these two pennies). Whoever takes the last penny wins. Is there a winning strategy for this game, and if so would you rather go first or second?

Hints

1. This has nothing to do with powers of 12.


2. If you haven't gotten this one yet, you haven't even tried it yet.


3. This one's a bit cheap--as in, it's too easy.


4. Think about writing these numbers in a different way.


5. Consider each intersection in isolation: how many strokes would this take? How many intersections are there?


6. Try this with 4 pennies first, and then 5, 6, 7, ...Try to find the pattern. Who always wins? The harder part is figuring out exactly how.

Source: http://focusedconsumers.blogspot.com/2010/08/entertaining-mathematical-puzzles.html