The Bat-and-Ball Puzzle, and a Discouraging Implication

I'm reading Daniel Kahneman's Thinking Fast and Slow. He suggests persons have two "systems" of thinking, and calls them "System 1" and "System 2."

System 1 operates automatically and quickly, with little or no effort and no sense of voluntary control.

1. System 2 allocates attention to the effortful mental activities that demand it, including complex computations. The operations of System 2 are often associated with the subjective experience of agency, choice, and concentration. (pp. 20-21)

Kahneman gives many problems and puzzles to illustrate the operations of these two systems. Here's one that shows how many people accept the conclusion of System 1 and don't go on to utilize System 2. He writes:

"One of the main functions of System 2 is to monitor and control thoughts and actions “suggested” by System 1, allowing some to be expressed directly in behavior and suppressing or modifying others. For an example, here is a simple puzzle. Do not try to solve it but listen to your intuition:
A bat and ball cost $1.10.
The bat costs one dollar more than the ball.
How much does the ball cost?" (p. 44)

Probably, the number '10' came to your mind. The correct answer, you think, is 10 cents.

But the correct answer is actually '5' - 5 cents. System 1 thinking intuits '10,' but when people stop here and succumb to lazy thinking, they err.

Interestingly, Kahneman writes:

"Many thousands of university students have answered the bat-and-ball puzzle, and the results are shocking. More than 50% of students at Harvard, MIT, and Princeton gave the intuitive—incorrect—answer. At less selective universities, the rate of demonstrable failure to check was in excess of 80%. The bat-and-ball problem is our first encounter with an observation that will be a recurrent theme of this book: many people are overconfident, prone to place too much faith in their intuitions. They apparently find cognitive effort at least mildly unpleasant and avoid it as much as possible." (p. 45)

"This experiment has discouraging implications for reasoning in everyday life." (Ib.)