True or False
Logic puzzles require you to think. You will have to be logical in your reasoning.
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.
HintHow many statements do you choose true, and how many statements do you choose false?
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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.
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Comments
Crazycriely
Oct 21, 2007
 This is wrong if 5 and 7 were both right...there'd be "at most 3 AND at most 4" true statements 
rngr4christ
Oct 21, 2007
 I was confused from get go. great teaser. 
MACK52
Oct 21, 2007
 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 
rehtaeh
Oct 22, 2007
 *stares blankly* I don't get it 
calmsavior
Oct 23, 2007
 It says "AT MOST", not "EXACTLY", hence at can be anything, but AT MOST it has to be a certain value. 
calmsavior
Oct 23, 2007
 If it says 'You chose "True" at most twice.' then it could be once, twice, or none at all. 
dreamlvr1432
Oct 28, 2007
 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. 
(user deleted)
Nov 07, 2007
 False to all of them. 
rt1819
Nov 11, 2007
 I am sorry, but that was too complicated! Teasers are supposed to be fun, that is the point! 
scallio
Dec 11, 2007
 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.

shenqiang
Dec 11, 2007
 "Consistent" is opposed to "contradictory". 
WCCope
Dec 27, 2007
 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. 
ana_virt
Jun 03, 2008
 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! 
Jota
Jul 10, 2008
 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. 
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