Abstract
Consider the following puzzles. Some of the solutions to these are discussed in detail in further chapters. For now, just ponder the puzzles themselves.
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Given two eggs, for a 100-story building, what would be an optimal way to determine the highest floor, above which an egg would break if dropped?
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Suppose you buy a shirt at a discount. Which is more beneficial to us: apply the discount first and then apply sales tax to the discounted amount or apply the sales tax first and then discount the taxed amount? What do stores do?
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If you have a biased coin (say, comes up heads 70 % of the time and tails 30 %), is there a way to work out a fair, 50/50 toss?
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A $10 gold coin is half the weight of a $20 gold coin. Which is worth more: a kilogram of $10 gold coins or half a kilogram of $20 gold coins?
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A farmer sells 100 kg of mushrooms for $1 per kg. The mushrooms contain 99 % moisture. A buyer makes an offer to buy these mushrooms a week later for the same price. However, a week later, the mushrooms would have dried out to 98 % of moisture content. How much will the farmer lose if he accepts the offer?
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If you heat a metal washer with a hole in the middle, what happens to the size of the hole?
If you want to build a ship, don’t drum up people to collect wood and don’t assign them tasks and work, but rather teach them to long for the endless immensity of the sea.
– Antoine de Saint-Exupery
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Notes
- 1.
A heuristic is an easy but imperfect way of answering hard questions. Emerging from experience, heuristics may provide satisfactory solutions via mental shortcuts that ease the cognitive load. The word has the same etymological root as Eureka, emerging from the Greek word heuriskein meaning to find or discover.
- 2.
Danesi M (2004) The puzzle instinct: the meaning of puzzles in human life. Indiana University Press, Bloomington.
- 3.
Poundstone W (2004) How would you move Mount Fuji?: Microsoft’s cult of the puzzle – how the world’s smartest companies select the most creative thinkers. Little Brown and Company, Boston.
- 4.
In hiring interviews, they are often known as impossible questions or Fermi questions based on estimation techniques popularized by the Nobel Prize winning physicist, Enrico Fermi. Some questions don’t have precise answers, e.g., “how many piano tuners are there in Chicago?” and some questions are to be approached with back-of-the-napkin style estimates, “what is the circumference of the earth?”
- 5.
When we have used this puzzle in class and elsewhere, we’ve seen the audience suggest 3 or 4 solutions before converging on the correct solution once they have analyzed and understood the actions described in this puzzle. This puzzle is discussed later in the book.
- 6.
STEM education is an acronym for the fields of study in the categories of science, technology, engineering, and mathematics.
- 7.
Daniel Kahneman gives a fascinating account of his Nobel Prize winning work in his book, Thinking, fast and slow, Farrar, Straus and Giroux, 2013.
- 8.
For an entertaining account of this skill please see Malcolm Gladwell’s book Blink: The Power of Thinking without Thinking, Back Bay Books, 2007.
- 9.
In 1966, the Mathematical Association of America (MAA) filmed a university class of Polya where he led a discussion on solving the five-plane problem (how many parts are created when a three-dimensional space is cut by five planes). The video recording, Let us teach guessing: A demonstration with George Polya, is highly recommended for both its content and to see the maestro at work. A local library may have a copy of this recording. At the time of this writing, it is also available online at http://vimeo.com/48768091
- 10.
An interesting phenomenon termed the Einstellung Effect (related to the confirmation bias) is partly due to the slothful nature of System 2 thinking. This effect is about our thinking tendency to stick with a familiar solution to a problem – the one that first comes to mind (via System 1) – and to ignore alternatives (which could arise from System 2 thinking). The interested reader is referred to the article Why Good Thoughts Block Better Ones, Scientific American (March 2014), 310.
- 11.
Perhaps the most famous of these errors is the conjunction fallacy as represented in “The Linda problem” originated by Kahneman and his collaborator Tversky. Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Which is more probable? (1) Linda is a bank teller or (2) Linda is a bank teller and is active in the feminist movement. Majority of those asked, including students from a top business school, incorrectly choose option 2, even though every feminist bank teller is a bank teller; adding a detail can only lower the probability.
- 12.
In addition to the pedagogical value discussed in this chapter and illustrated in the remainder of this book, solving puzzles also provides mental health benefits. See the book The Playful Brain: The Surprising Science of How Puzzles Improve Your Mind, Riverhead Trade, 2010. Neurologist and neuropsychiatrist Richard Restak and master puzzle creator Scott Kim discuss how puzzle-solving improves three aspects of our mind: memory, perception, and cognition.
- 13.
Wing J (2006) Computational thinking. Commun ACM 49(3):33–35.
References
Bilalić M, McLeod P (2014) Why good thoughts block better ones. Sci Am 310:74–79
Danesi M (2004) The puzzle instinct: the meaning of puzzles in human life. Indiana University Press, Bloomington
Gladwell M (2007) Blink: the power of thinking without thinking. Back Bay Books, Boston
Kahneman D (2013) Thinking, fast and slow. Farrar, Straus and Giroux, New York
Poundstone W (2004) How would you move Mount Fuji?: Microsoft’s cult of the puzzle – how the world’s smartest companies select the most creative thinkers. Little Brown and Company, Boston
Restak RM, Kim S (2010) The playful brain: the surprising science of how puzzles improve your mind. Riverhead Trade, New York
Wing J (2006) Computational thinking. Commun ACM 49(3):33–35
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Meyer, E.F., Falkner, N., Sooriamurthi, R., Michalewicz, Z. (2014). Motivation. In: Guide to Teaching Puzzle-based Learning. Undergraduate Topics in Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-6476-0_1
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