Here’s an interesting math problem I came across some time ago. Multiple times actually, in real life.
Suppose you and a friend are going to the cinema and each ticket costs $6. You arrived early so you paid for both the tickets. When your friend arrived, you both went to get some popcorn and saw the combo meal consisting of a bag of popcorn and two drinks for $6 dollars.
Since your friend owes you $6, is it fair for your friend to pay the $6 combo meal and call it even?
You might be tempted to say yes. After all, your friend owes you $6, and now he’s paying that $6 for the combo meal. Why not just call it even?
You’re thinking too fast. It’s just like the bat and the ball problem.
If a bat and a ball cost $1.10, and the bat costs $1 more than the ball, how much does the ball costs?
It’s very tempting to answer $0.10, isn’t it? But that’s wrong. If the ball costs $0.10, then the bat, costing $1 more, would cost $1.10, giving a grand total of $1.20.
The correct answer is $0.05, which means the bat would cost $1.05, giving the correct total of $1.10.
Similarly, in the previous example, you paid a total of $12 for both the tickets. Your friend only paid $6 for the combo meal, so no, you can’t call it even. To make it even, your friend has to pay you another $3 so that both of you paid a total of $9 each.
Anyway, that is the mathematically correct way of splitting the bill. If you don’t mind paying for your friend, then you are free to split it however you wish, as sometimes, you might be in a generous mood.
Or perhaps you might want to test how mathematically-minded your friends are and inform them of this fallacy, preferably when you are the one paying for the $6 combo meal.
Don’t fall into the trap of thinking too fast. Like the two above math problems, there can sometimes be an intuitively wrong answer that we fall prey to if we’re not careful.