# The Bat, Ball Problem

September 15, 2019**A baseball bat and a ball cost $1.10 together, and the bat costs $1.00 more than the ball, how much does the ball cost?**

**
**Did you arrive at 10 cents?

If so, you’d be *wrong*.

Here’s the solution:

Although $1.00 + $0.10 does equal $1.10, if you take $1.00 – $0.10 you get $0.90, but the problem requires that the bat costs $1 more than the ball.

So, the ball must cost $0.05, and the bat must cost $1.05 since $1.05 + $0.05 = $1.10

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Still not convinced? You can use algebra to solve the problem:

First, let’s set up the equation:

x + ($1.00 + x) = $1.10

$1.00 + 2x = $1.10

2x = $1.10 – $1.00

2x = $0.10

Finally, solve for x:

**x = $0.05**

Check your work:

x + ($1.00 + x) = $1.10, so

$0.05 + ($1.00 + $0.05) = $1.10

## Why does the bat-and-a-ball problem have any significance?

If you answered 10 cents you are inclined to believe in religion. If you answered 5 cents you are inclined to disbelieve. Why? Because, according to research reported in the journal Science, the 10 cent answer indicates that you are an intuitive thinker, and the 5 cent answer indicates that you solve problems analytically, rather than following your instincts.

From Psychology Today:

Their study of 179 Canadian undergraduate students showed that people who tend to solve problems more analytically also tended to be religious disbelievers. This was demonstrated by giving the students a series of questions like the one above and then scoring them on the basis of whether they used intuition or analytic logic to reach the answers. Afterward, the researchers surveyed the students on whether or not they held religious beliefs. The results showed that the intuitive thinkers were much more likely to believe in religion.

… Professor and Chairman Terrence Reynolds of the Department of Theology at Georgetown University finds it plausible that analytic thinking could make religious belief more difficult. “If one assumes that all rationality is tied to what we know directly through the five senses, that limits our understanding of meaning questions. Religion tends to focus on questions of meaning and value, which may not be available through analytic verification processes… by definition God is a being that transcends the senses.”

**Quick Poll** – What was your answer, and do you believe/disbelieve in religion?

### Another interesting puzzle, which you may or may not consider tricky:

In a lake, there is a patch of lily pads. 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 of the lake?

**A)** 24 days

**B)** 47 days

**C )** 48 days

**D)** 49 days

**E)** none of the above (state your answer and why)