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The Baseball Conundrum

July 30th, 2014 by Math Tricks | Filed under Brain Teasers.



The Baseball Conundrum

Here is a brain teaser that has taken several forms in the past, but I remember it as a baseball-themed enigma. Think about it carefully. You may think that your answer is a logical deduction, but it may very well be wrong. Also, if you do come across a store that charges such high prices, you may want to consider shopping elsewhere! So, anyway, the problem is:

If a baseball and baseball bat cost $110, and the baseball bat costs $100 more than the baseball, how much does the baseball cost?

The answer and explanation are below, but if you want a hint as to how to solve this puzzle, try to use a little bit of algebra in your reasoning – and try to solve it by using pen and paper!





























Answer and Explanation

The cost of the baseball is $5.00.

How did I solve this problem?  I wrote it out so that I can visually see what is going on (I can’t see it in my mind very well because it is clouded with such unsavory thoughts!):

ball + bat = 110

bat = 100 + ball

by substitution:

ball + 100 + ball = 110


ball + ball + 100 = 110

2 balls + 100 = 110

2 balls = 110 – 100

2 balls = 10

And so:

1 ball = $5

So the real question here is, what is so special about the bat that would justify a price of $105?!!





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5 Responses to “The Baseball Conundrum”

  1. David | 2/08/14

    Where did the second ball come from?

  2. Will | 2/08/14

    My question is why does this question wind up here when the answer is so simple. This site has some questions that just melt my brain

  3. Steven Pomeroy | 11/08/14

    David, that is just some applied algebra that was used to derive the answer. There are not two balls in the example, but the algebra a substitution method that equated: bat = 100 + ball.

    If you go line by line carefully, you will see how this method helps you solve the question.

  4. Steven Pomeroy | 11/08/14

    Hi Will,

    This is a classic problem that many are confused by; it is a great example on how algebra can be employed to solve it.

  5. Steve | 20/08/14


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