### Brain Teasers

# True or False

Choose true or false to these statements, and your choices must be consistent.

1. You chose "True" at most once.

2. You chose "False" at most once.

3. You chose "True" at most twice.

4. You chose "False" at most twice.

5. You chose "True" at most three times.

6. You chose "False" at most three times.

7. You chose "True" at most four times.

8. You chose "False" at most four times.

9. You chose "True" at most five times.

10. You chose "False" at most five times.

1. You chose "True" at most once.

2. You chose "False" at most once.

3. You chose "True" at most twice.

4. You chose "False" at most twice.

5. You chose "True" at most three times.

6. You chose "False" at most three times.

7. You chose "True" at most four times.

8. You chose "False" at most four times.

9. You chose "True" at most five times.

10. You chose "False" at most five times.

### Hint

How many statements do you choose true, and how many statements do you choose false?### Answer

You can't choose true in both statements 1 and 2, at least one of them must be false. Similar logic exists in statements 3 and 4, and 5 and 6.Statements 7 and 10 are contradictory, you must choose one of them true and the other false. Similar logic exists in statements 8 and 9.

Therefore, you choose "false" at least 5 times and "true" at least 2 times. By trial and error you see that statements 5, 7 and 9 are true, and the others are false.

Hide Hint Show Hint Hide Answer Show Answer

## What Next?

View a Similar Brain Teaser...

If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.

### Solve a Puzzle

## Comments

This is wrong if 5 and 7 were both right...there'd be "at most 3 AND at most 4" true statements

I was confused from get go. great teaser.

I don't see your logic? The only way I can justify the statements is 1 is true the rest false. If as you say 5+7+9 true rest false you can't have 7+9 true as that makes three trues and seven falses which cancels 7+9

*stares blankly* I don't get it

It says "AT MOST", not "EXACTLY", hence at can be anything, but AT MOST it has to be a certain value.

If it says 'You chose "True" at most twice.' then it could be once, twice, or none at all.

When the instructions said "Choose true or false to these statements, and your answers must be consistent", I took that to mean it had to be the same to every question, consitently true OR consistently false..which would make the answer false. Was not aware that you were looking to find which particular ones were true or false. The instructions are not clear in that respect.

Nov 07, 2007

False to all of them.

I am sorry, but that was too complicated! Teasers are supposed to be fun, that is the point!

Well, I had fun AND got the correct answer!

I do have to admit though that I found myself wondering what you meant by the answers needing to be consistent. Perhaps it should have said "your answers must be accurate". Anyway, I still figured it out and enjoyed myself along the way.

I do have to admit though that I found myself wondering what you meant by the answers needing to be consistent. Perhaps it should have said "your answers must be accurate". Anyway, I still figured it out and enjoyed myself along the way.

"Consistent" is opposed to "contradictory".

consistent in this case means one answer can't change the value of another, or if it does you must change all the values until they are all correct at the same time.

What about this: I simply choose "false" for all the statements. Therefore, I've got ten falses, and obviously none of the stataments is true!

Great teaser!

You can't choose false for each statement because then you would have chosen true zero times and therefore statements 1,3,5,7,9 should all be true.

As a previous comment stated, "at most five times" means 0, 1, 2, 3, 4, or 5 times.

You can't choose false for each statement because then you would have chosen true zero times and therefore statements 1,3,5,7,9 should all be true.

As a previous comment stated, "at most five times" means 0, 1, 2, 3, 4, or 5 times.

After rewriting the problem as a set of relations of binary variables, I used 'scip' to solve it. For anyone interested, the model that I used can be found at https://pastebin.com/1ZiWWitU

To post a comment, please create an account and sign in.

## Follow Braingle!