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# How many balls are their?

## Question

At a circus fair their was a booth, where you had to guess the amount of balls in each cup. Their were four cups. They all had the same amount.In front of each cup it said how many balls were in each. In front of the first - "One or four", the second - "Two or one". The third- "Three of four." The fourth- "Two or four". Only one statement was true. How many balls were their in total?

(i hope i did this right) 12

(i know how this can sound sexual, so you don't need to comment on that, i just did.)

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hmm.

I like this one.

I thought it was three until I read the spoiler.

Cool, keep it up

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hmm. Cool.

Do you know any others?

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Most of them in here require pictures, but I'll search for some that don't.

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Change the signs on the cups to their opposite.

The changed statements give the following possible number of balls in each cup.

Three of the statements are now true.

[2] _ _ 3 4
[3] 1 2 _ _
[4] 1 _ 3 _
`[1] _ 2 3 _`

The only number that three statements agree upon is 3.

There are 3 balls in each cup, 12 in all.

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That is correct, although i fail to see how that got you got it the way you did....

Their is a much simpler way...

But to each their own.

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That is correct, although i fail to see how that got you got it the way you did....
Three negated signs are true.

The correct number is thus named three times, on cups 1, 2 and 4.

Couldn't be much simpler than that.

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Oh. Duh!

I looked at the answer wrong.

So I was right...

cool

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That is correct, although i fail to see how that got you got it the way you did....

Three negated signs are true.

The correct number is thus named three times, on cups 1, 2 and 4.

Couldn't be much simpler than that.

I know, but that you explained yourself in your first post in this thread confused me is all.

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Change the signs on the cups to their opposite.

The changed statements give the following possible number of balls in each cup.

Three of the statements are now true.

```[1] _ 2 3 _

[2] _ _ 3 4

[3] 1 2 _ _

[4] 1 _ 3 _```

The only number that three statements agree upon is 3.

There are 3 balls in each cup, 12 in all.

Gee, bonanova, usually you are good at impressing me with your mathematical prowess. However, this time it seems that you decided to travel south to get to the north pole.

If only one statement is true, then only one of the signs has the correct answer. The only number to appear once is "three". That seems like a much more direct way to solve it to me.

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that's how I solved it.

I just thought I was wrong for a moment because I answered in how many balls were in each cup.

Not how many there were in total

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this time it seems that you decided to travel south to get to the north pole.
Nicely put.

Acutally I first solved it by going North. It just seemed more crisp to deal with positive statements.

Anyway, I've retired and have time to travel.

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