PROBLEM. A bat and a ball cost $1.10 together. The bat costs $1 more than the ball. How much does the ball cost?
SOLUTION. The puzzle is simple but proved notoriously tricky to solve purely for psychological reasons. It intentionally misleads a solver into making a wrong decision by creating false associations. The puzzle was created by Yale University professor Shane Frederick, who specialises in consumer behaviour patterns. It illustrates how clever wording can influence our opinions and guide our decision-making. Nobel laureate in economics Daniel Kahneman used this puzzle in his popular book Thinking, Fast and Slow, exploring two modes of our brain functions: the intuitive fast and the analytical slow.
If you have seen this puzzle before, you know the answer is 5 cents. But if you haven't, your first reaction will probably be 10 cents. Ultimately, that's what half of Harvard University students said when pressed for a fast answer, and you can hardly call them simple. These students boast the highest IQ levels and can handle far more sophisticated problems. Still, they fell for a trap because fast thinking tends to pick up superficial clues, which can be misleading.
The author uses visual object recognition to lure a solver into error. The scientists have discovered that our brain has two modes. One is autopilot, which helps with simple tasks requiring no deep thinking. Another mode is responsible for analytical reasoning, which solves more complicated tasks. The autopilot mode prioritises visual clues and matches them with certain actions. Below are three road signs displaying a common figure of the man with a spade. Drivers will slow down automatically at each of them because their autopilot mode will immediately connect this figure with the roadwork ahead.
A solver will start the solution in analytical mode. The puzzle asks about the ball, so a solver will start processing the data relative to the ball, revising it backwards from end to start. The bat costs $1 more than the ball, therefore, the ball costs $1 less. Next, a solver will come to a figure of $1.10, which looks similar to $1.00. An autopilot mode kicks in, connecting two figures with the subtraction operation. As a result, a solver's brain will translate the information as "total cost is $1.10, and ball costs $1.00 less". The autopilot mode always runs in the background of our brain by default, ready to spring into action when a fast response is needed. The next step seems obvious: the ball's price must be $1.10 - $1.00 =$0.10.
However, given more time, a solver will realise that the ball is $1.00 less than the bat, not the total cost. I will rephrase this puzzle in a way that makes its conditions clear:
The sum of bat and ball is $1.10
The difference is $1.00
Now, we can see that we have two unknowns and two equations. I'll use visual object recognition to find the solution and show how helpful this brain function is when no tricks are involved.
The correct answer to this puzzle is: the ball costs $0.05, and the bat costs $1.05.
The author intentionally chose simple figures $1.10 and $1.00 to trigger an automatic response. The puzzle below is practically identical; only the figures don't look similar. You won't trick a Harward student into the wrong answer with this puzzle; the autopilot mode will not overpower the analytical one.
The sum of the mother and daughter's ages is 50. Mother is 30 years older than daughter. How old is the daughter?
Neuroscientists discovered that the autopilot mode is real and run by a network of brain cells called the default mode network (DMN). Similar structures were found in the brains of animals, with primates exhibiting the most advanced versions. However, even the primate can't compete with human DMN, exposing a significant gap between them. Research into the second mode proved difficult. Animals don't have this mode; they can't build logical deductions when deep analysis is required. Experiments on the human brain raise ethical issues. Besides, as individuals, we solve logical tasks differently, using a creative approach based on personal experiences. The different paths activate different brain cells, making it difficult to establish stable patterns that could generalise this mode.
Artificial Intelligence (AI) is modelled on our autopilot mode. When we run through text for relevant information, we look for the keywords, a function adopted by Google and other search engines. The AI can recognise the links between letters and sounds; this ability is used in text-to-speech converters. Humanoid robots respond to verbal and visual stimulants and connect them with actions. This advantage allows them to perform tasks we do without engaging in deep thinking, like working in warehouses, serving food, and driving cars. They can even dance better than you and me, as proven by the American engineering company Boston Dynamics. But they will never match the brilliance of the human mind, capable of thinking outside the box, generating fresh ideas and making new discoveries. These qualities distinguish us from the rest of creation and make us what we are: humans.
Boston Dynamics Robots Dance to "Do You Love Me", The Hollies
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