If a baseball and a bat cost \$1.10 together, and the bat costs \$1.00 more than the ball, how much does the ball cost?

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

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

1. Also if one answered 10c, or just angrily gave up it could be that one has not been taught to think analytically.

I confess 10c was all I could think, Although I had expected the answer not be the one which first came to mind.
I most certainly do NOT believe in such things as religion.
Was I in fact thinking analytically but with no real mental “tools” to gain any traction? (welcome to my nightmare)
All I needed was the tools to figure out what I’d suspected. thank you for the insight.
why oh why wait until higher education to introduce this to people!! (at least in my day anyway)

2. 1.05 – 5 = 1.00

They said the bat costs 1.00 MORE than the ball. So the ball is 5 cents. I’m not good at mathematics but I pay attention to the way words are used.

3. RE the lake question…in my book the answer is e…NOTA. Why you ask? To simply say that it takes the patch 48 days to fill the lake, and the patch doubles in size each day; the pool of answers could still be quite infinite because you are measurably omitting the rate of patch growth in relationship to the surface size of the lake itself…on proportion the answer of 47 marginally works but only if one “assumes” each day of patch growth is identifcal. however it works in whole when you inlclude the size of the lake.

• You’re provided 2 axioms. 1. that each day the patch doubles in size. 2. It takes 48 days to cover the entire lake. From these, you can make the assumption that on the 48th day, the patch has doubled exactly to cover the whole lake otherwise it would conflict with the first axiom. So yes, you’re meant to assume.

4. The 10cent ball may not be the answer you were looking for, but it IS an answer that fits the question.
eg Q. What two numbers when added together make 5?
A. There can be as many answers as you want, depending on whether or not you want to delve into fractions .

• That is what they are asking you could say no its .4999… Your wrong for saying its 5 because saying 60degrees is the same as 59degrees59’59”

• 10 cents is not an answer that fits the question.

Let’s say the ball cost 10 cents, i.e. \$0.10. As the bat costs \$1 more than the ball, the bat would cost \$1.10, right? The bat and the ball would then cost \$1.10 + \$0.10 = \$1.20. So 10 cents is not an answer that fits the question.

Let’s say the ball cost 9 cents, i.e. \$0.09. As the bat costs \$1 more than the ball, the bat would cost \$1.09. The bat and the ball would then cost \$1.09 + \$0.09 = \$1.18. So 9 cents is not an answer that fits the question.

You can do similar calculations for other answers that you believe fit the question. Only if the sum turns out to be \$1.10 you have found an answer that fits the question.

Your Q and A is correct, but that Q is not parallel to the bat and ball question.

5. Furthermore. If asked what is the opposite of ‘right’, is the correct answer ‘left’? or ‘wrong’?

6. There are two two correct answers to this question. The way that the question is worded does in no way suggest that the numbers have a second mathematical requirement. (the subtraction check.) I think that this is a very misleading analysis and proves nothing more that the most obvious answer is obvious.

• There is only one answer. The bat must cost \$1.00 MORE than the ball with a combined total of \$1.10. Simply take the dollar out (because that will be added to the price of the bat ) and then split the remaining \$0.10. It seems tricky at first…but THAT’S THE FUN of the question!!!

• Guess wat
1.05>1.00
And .05 needs .05 over a dollar added to it to equal 110
Whcih you need to do because 1.05 is not a dollar
1.00 is

• That is not what the question is saying the question is the bat is exactly one dollar more than the ball so if the ball is \$20 the bat would be \$21 the same way as if the ball is 5 cents the bat would be 1.05 which equals 1.10

• It’s just one dollar more. If the ball were 10 cents and the question says one dollar more it’s 10 cents plus one dollar more equals 1.10 dollar. The bat by itself is then already 1.10 dollar while the total should be 1.10. So 10 cents for the ball is wrong.

• The bat isn’t 1 dollar, it’s one dollar more. So if the ball was .10 it would be .10 and a dollar more (=1.10). You seem to be fixed on the fact that the bat is 1 dollar which is wrong, it’s one dollar more.

• There is ONE correct answer, the ball and the bat cost 1.10\$ TOGETHER.
First thing you have to realize is it’s not really about the math here, the answer can be found in the phrasing of the puzzle.

If the ball and the bat would cost only 10 cents together how much do they cost each?

0,5 cents each right?

But the bat costs 1\$ more, so the bat costs 0,5 cents + 1\$ more = 1.05\$
+ 0,5 cents for the ball, equaling a total of 1.10\$ together.

EDIT:Ok, just realized this thing is 3 years old…

7. I agree with Jason and “the way that the question is worded”! May be obvious that it’s precisely \$1.00 MORE, not \$1,05 more!

• But it is not \$1.05 more. If the bat was \$1.00 and the ball was 10 cents, you’d = \$1.10 Right? Wrong. Because \$1.00 – \$0.10 = \$0.90. And it has to be 1 dollar more than the ball. If you were to have the cost of the bat be \$1.00, it would be mathematically impossible to solve. So, english wise, the problem does not apply that it can be over \$1. But mathematically, it is saying you are going to have to fluctuate the cost of the bat.

8. the price of the ball could be 9,8,7,6,4,3,2,1 cents and does not have to be 5 cents. all the other denominations are equally valid.

• It has to be exactly one dollar more so if it was 9 cents that would be 1.09+.09=1.18 that does not equal 1.10 the only way for it to equal 1.10 is to divide 10 by 2 and get 5 so that 1.05+.05=1.10

• if bat costs 1 dollar how much is ball gona cost if its 1 dollar cheeper than the bat.

or and if we run with the answer from above aka 0,05 then

0,05+1,00=1,05

• Wrong. The total is \$1.10

If the ball was 9 cents, the bat would be \$1 more, making a total of \$1.09, not possible. There is only 1 answer. \$1.05 + 0.5 (ball) =\$1.10

• wrong.. the bat and the ball together cost 1.10. Separately the bat costs 1 dollar more than the ball. meaning the bat has to cost anything above 1 dollar.. it doesnt have to be 5 cents.. it can be 1. No one said the ball costs 10 cents. It doesnt have to be divided in half. The bat can be 1.01 its above 1 dollar and the ball is 0.09. Put both together you get 1.10. kys.

• dude no. It’s a dollar more, not more than a dollar.
0.09 + 1.09 = 1.18
It has to be 5 cents.

• dollar more than the ball. Together 1.10. separate bat costs a dollar more. 1 dollar out of equation. that leaves 10 cents. 2 items split 50 50? because its MORE that means it has to take half of the balls price. 1 dollar +0.05. THen it is exactly 1 dollar more than the ball. Crappy trick math.

9. I’m a disbeliever of any religion. Apparently I’m not very good at critical thinking since I got the baseball and bat answer wrong and couldn’t figure it out. I suck at academic stuff too.

I think aspiring to figure out the truth with whatever one’s critical thinking ability can also be a strong factor in whether he/she believes in a religion. Since many people are by default average in intelligence, it maybe more significant than critical thinking skills.

10. my mind said 10 cents but i knew it was too easy but i didnt know how to figure it out.. what does that say about me?

• technically it could be any time on the 47th day… on the 48th day the lake was 100% covered but without knowing the area of the first patch or the area of the lakes surface for all we know on day 47 the lake was 99% covered.

lets make it simple and put it like this. if your lake is 100km^2, and your lily patch started at 20km^2 at midnight Day one and doubled as in the first riddle.

-the start second day will be 40km^2 (40%) covered
-the start third day will b 80km^(80%) already more than half the lake (as the 47th day may have been) if this doubled again it would be much larger than the lake.
-with only 20km^2 left (20%) the lake will be completely covered by 6am on the fourth day. thus taking 3.25 days to cover.

now that was to make it simple. the original riddle could literally be anywhere from 47-48days to cover the lake and could be any real number between the 2.

for the sake of the riddle assume everything worked out exactly it would be the
47th day

11. I got 1.10 but I new it was wrong. I wanted to do the math and figured the word “more” was relevant. Not very religious

12. .10 CENTS IS THE CORRECT ANSWER
Bat is one dollar more than the ball
The correct equation:
1.00 should be subtracted from the total sum of
1.10 which is the total sum we are asked to work with. We were not asked to work with the total sum of 1.00 (as you equation erroneously states) but one dollar MORE than the combined total we are given.
1.05 does not equate to being 1.00 more. It equates to being 1.05 more than the bat when you are given a total sum of 1.10 to work with. This is BS and trickery and why many people do not fully trust mathmatics and science. I believe in a creator god btw. The evidence… I walk outside my front door to a vast universe that was created by something that is completley incomprehensible to the limitations of the human mind. Only the immense ego of man would somehow think they have it all figured or CAN figure it all out. I do not believe in organized religion but i definately believe in.a higher power.. I got two out of three questions right. I’ll make that three with the correction of your bogus #1 answer.

• … but \$1.00 is only 90 cents more than 10 cents.. to cost \$1.00 more the bat would be 1.05 and the ball would be .05 … equalling \$1.10.

• We are being given a sum for the Total price for the combined items. That sum is not 1.00. The sum we are given is 1.10. We are asked to decide what each items cost is based on that sum with the caveate that the bat is one dollar more.

• ok.. but if you have 5 cents and I have one dollar more than you… I would have to have 1 dollar and 5 cents, or I would not have 1 dollar MORE than you..

13. “You believe in religion”

And atheists believe in the talking snake on an exoplanet near the Andromeda galaxy.

This is sincerely the stupidest conclusion anyone who’s ever conducted a reasearch has come to.

• This isn’t research into the belief of religion, it’s just a statistic that happens to match on people choosing a particular answer.

14. I can understand initially getting the answer wrong, but I can’t understand continuing to argue the point after it is explained in the article as well as multiple times in the comments.

• Because the answer presented is wrong given the question presented.

It even specifically points it out at the start of the article. \$1 added to something that makes up \$0.10 means that what \$1 was added to was \$0.10

The question is worded with the term that you ADD \$1 MORE to the cost of the ball.

Which, by any analytical standard, equates to the ball costing \$0.10

“B-but the b-ball equals!”

\$1 more than something means you ADD a dollar to that something.

If the question said that 2 balls equals \$0.10 then it would make sense.

It appears those arguing, like yourself, continuously rely on the claimed answer rather than addressing that everyone is answering the question asked. Which equates to the ball costing \$0.10

• But together they cost 1.10 dollars. So if it costs 1 dollar more than the ball together it would be 1.20. We dont know how much the bat costs only thats 1 dollar more than ball, hence their math is solid.

15. I understand the algebra used to determine the answer to the question. Makes sense. Here’s another riddle: If you walk into this store, grab a \$1 bat, and .05 ball, and put them on the counter (assuming no taxes), can you give the clerk \$1.05 to buy them?

• Uh. Yeah. That isn’t a riddle that’s just adding 1 and .05
The original problem can be done without the algebra, you just realize that the change of the 2 items together has to equal 10 cents

16. What a lot of you don’t seem to be getting is that the bat is a dollar more than the ball not a dollar more than the sum of the ball and the bat. Go and reread the question and you’ll see that that’s where you came unstuck.

17. Sorry I phrased that wrong- I meant to say the bat is a dollar more than the ball but the sum of the ball and the bat isn’t a dollar more than the ball. Just had a major dyslexic moment there…

18. Who makes this crap up? I mean, really? There are TWO points to this ridiculous equation – their point and the actual mathematical equation. Neither answer is wrong.

19. None of this was making sense and even after reading the comments I was getting even more confised, then found an answer on a different site that explained it in a more simple way. So here goes… “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.”

For me, it really came down to fact that no one here stated the problem of arriving at an incorrect total of \$1.20. When I saw that, the light came on for me. For the bat to be a dollar MORE, you have to add a dollar to the cost of the ball to arrive at \$1.10 total.

• Your last sentence is still falling into the “intuitively correct” thinking trap this puzzle exposes so well.
Adding a dollar to the cost of the ball does *not* arrive at the total; it arrives at the cost of the bat.
You have to add the cost of the ball to that of the bat TWICE to arrive at the total cost:
once to get to the cost of the bat, then again to get at the total for bat and ball.

• Correct. You definitely wouldn’t be going to Harvard. Not even sure you’d be going to the University of Phoenix online if they heard that business plan.

20. together 1.10. Separately the bat costs 1 dollar more than the ball. Meaning the bat can be 1.00000000000000001 for all i care the ball will cost the rest. Put together it’s still 1.10.

21. The patch doubles in size every day and so on the 47th day the patch will be half the size it is on the 48th day

22. When i first saw this question, i thought it is 10 cents but i look at the answer, its 5 cents. It took me like 30 mins to figure out how its 5 cents and i found out. Its because the question said “If a baseball and a bat cost \$1.10 TOGETHER and the bat cost \$1.00 MORE then the ball, how much does the ball cost?” Its 5 cents because the bat is \$1.05 and the ball is 5 cents which makes a total of \$1.10 cents so the answer is 5 cents.

23. I figured multiple times that it was \$1.10 just because it seemed right. Couldn’t really find the reason, though. Then I thought it was 0.10 but I knew that answer would have been too easy. Then I ended up just giving up. Little did I know…

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