A riddle that stumps most people when first attempted is the baseball-bat problem.

Here it is:

“A bat and ball cost $1.10.The bat costs one dollar more than the ball.
How much does the ball cost?”

baseball

Of course, if you are familiar already with this brain-twister, then you’ll know the answer is 5 cents.  Or is it?

The reasons for it being 5 cents are as follows:

If the bat is 1 dollar more than the ball and the total of both is $1.10, then 1 dollar more would be $1.05 because $1.05-$.05= exactly 1 dollar more.

But then why do so many people get it wrong? In fact, it has been stated that 50% of Harvard, Princeton, and MIT students get this question wrong (Theblaze.com).

In that same article^, Daniel Kanehman gives his explanation as to why people intuitively choose the incorrect 10 cents.

 …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.” (Thinking Fast and Slow)”

However, I have another explanation: Semantics.

Almost every word in a language is polysemous. Polysemy means that there are more than one meaning embedded in a word.

Take for example the word “man”.


Man

  1. The human species (i.e., man vs. animal)
  2. Males of the human species (i.e., man vs. woman)
  3. Adult males of the human species (i.e., man vs. boy)  (Wikipedia: Polysemy)


Or even the preposition”through”

Through

  1. In between (ie. go through the bushes)
  2. Go inside and outside (ie. go through a tunnel
  3. Finished/over


And each of the sub-meanings of “through” can even have either spatial or motion characteristics. (ie. The rods go through the ceiling vs. the train went through the tunnel).

So, with polysemy in mind, what is the word in question in this riddle?

more

That’s right – “more”!

“More” has several polysemous definitions, as well. 

Don’t believe me? Look it up in a dictionary.

Here is from dictionary.com:

adjectivecompar. of much or many with most as superl.

1.

in greater quantity, amount, measure, degree, or number:

I need more money.

2.

additional or further:

Do you need more time? More discussion seems pointless.
noun

3.

an additional quantity, amount, or number:

I would give you more if I had it. He likes her all the more. When I could take no more of such nonsense, I left.

4.

a greater quantity, amount, or degree:

More is expected of him. The price is more than I thought.

5.

something of greater importance:

His report is more than a survey.

6.

(used with a plural verba greater number of class specified, or the greater number of persons:

More will attend this year than ever before.
adverbcompar. of much with most as superl.

7.

in or to a greater extent or degree (in this senseoften used before adjectives and adverbs, andregularly before those of more than two syllables,to form comparative phrases having the sameforce and effect as the comparative degreeformed by the termination -er):

more interesting; more slowly.

8.

in addition; further; longer; again:

Let’s talk more another time. We couldn’t standit any more.

9.

FurtherMORE, the phrase “more than” also breaks down to several meanings. Since dictionaries don’t normally allow phrase searching, type this one into your thesaurus.

Here is from thesaurus.com:















So, what is the confusion in this question? I will break down the common interpreted meanings of the same question that lead to the two different answers $.05 and $.10.

“A bat and ball cost $1.10.The bat costs one dollar more than the ball. (=the bat is an extra dollar of the cost of the ball)
How much does the ball cost?”

“A bat and ball cost $1.10.The bat costs one dollar more than the ball. (=the bat is supplementary/besides the ball 1 dollar)
How much does the ball cost?”

As you can probably tell, the meaning changes slightly depending on the way you interpret “more”.

In the first example, the commonly accepted answer is correct when considered that the bat is an extra dollar of the cost of the ball. 

However, if “more than” is interpreted as “supplementary” or “besides” as the phrase “more than” often is interpreted (i.e. “You need more than a windbreaker if you want to live in Scandinavia”) , then you will get the answer for the ball = $.10.

Look again:

    “A bat and ball cost $1.10.
     The bat costs one dollar in supplement to the ball.

     (The bat costs one dollar besides the ball.)
     How much does the ball cost?”
This radically changes the equation, doesn’t it?

Rather than an “extra” meaning in which you would add $1.05 to $.05 to get the one dollar more that is the crux of the solution, now we have the meaning of supplement or besides.

So if the ball is 10 cents, then a supplementary (or besides) amount of one dollar would come out to ($.10 ball besides $1.00 bat)
bat base-ball

Bat (1 dollar)                    Besides                        cost of ball($.10)


And this is the reason why the ball costs both $.05 and $.10 and why so many people are tricked by this question.

 

So again, it all comes down to semantics and how we interpret the words we read. While Kahneman’s point might still hold true, in that we go towards the easiest answer, what he failed to mention was the semantic ambiguity which allows people to make the easy choice. 

So don’t feel bad, whoever got it wrong! 🙂