1. The Bat and Ball Problem
A bat and a ball together cost $1.10. The bat costs $1 more than the ball. How much does the ball cost?
Did you guess 10 cents?
Take a minute to think about it. Many people respond by saying that the ball must cost 10 cents. Although this response intuitively springs to mind, it is incorrect. If the ball cost 10 cents and the bat costs $1.00 more than the ball, then the bat would cost $1.10 for a grand total of $1.20. The correct answer to this problem is that the ball costs 5 cents and the bat costs — at a dollar more — $1.05 for a grand total of $1.10.
2. The Widget-Making Machine Problem
If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machine to make 100 widgets?
Did you guess 100 minutes?
It would take 100 machines 5 minutes to make 100 widgets. Your gut might tell you the answer is 100 minutes. From the question, we know that it takes 5 minutes for 1 machine to make 1 widget. Thus, it would take 5 minutes for 100 machines to make 100 widgets.
Does it make more sense now?
3. The Size-Double Lily Pad Patch Problem
There is a patch of lily pads in a lake. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half the lake?
Did you guess 24 days?
The lily pads would cover half the lake in 47 days. You might have guessed 24 days. It seems intuitive to halve the number of days because you’re halving the size of the lilypad patch. But if the area of the lake covered in lilypads doubles every day, it would only take one day for it to go from being half covered to fully covered. Take one day away from 48 days and you’re left with 47.
Cover photo | Shutterstock|Pathdoc
