1st weighing: ( if the fake is lighter )
7-6
then the lighter of the 2 is broken up and you weigh again
3-3 if 6 is lighter: 4-3 if 7 is lighter
finally the lighter of the 2 is tested again:
2-1 for 3; 2-2 for 4
Sorry, you can't just assume that the fake coin is lighter when the problem states that it weighs differently. Assume exactly that and you have something real to solve :-)
Touche' I realized that upon posting
Warning:This answer probably doesn't give the correct answer to the 13 coins question so you can only use what I did as a clue or as a I shouldn't do this tactic thing.Good luck with this question and I never cheated :D
First we give all the coins numbers.We put 1-4 to first side and 5-8 to second side.
1A.Let's assume the 1-4 side was the heavy side.Now we exchange numbers 3-4 with numbers 5-6 and exchnge 8 with 9 and finally we exchange 3 with 13 so it looks like 1-2-5-6 and the other side 13-4-7-9.
2AA.Assuming the 1-2-5-6 part is still heavier,we now know that 13-4-7-9 aren't fake because they switched sides yet the balance didn't change.We know that 8 is real because it was exchanged with a real coin and still didn't effect anything.
3AA.We know that 1-2-7 is fake.But we also know 1-2 are fake because they can be heavier but 7 might be fake because it might be lighter.So we put coin 1 in the first side and the coin 2 in the second.If they are equal 7 is fake.If 1 is heavier 1 is fake.If 2 is heavier 2 is fake.
2AB.Now let's assume 13-4-7-9 part is heavier.This means 1-2-7 is real because the balance changed.1-2-7 didn't change positions while we know 9 and 13 are real coins.
3AB.So 4-5-6,any of them can be fake.But we do the same thing.5 and 6 were in the same side while being weighed and they were heavier.So all we have to do is to weigh 5 and 6.If 5 is heavier it means 5 is fake.If 6 is heavier 6 is fake.If they are equal 4 is fake.
2AC.There is also another chance while weighing 1-2-5-6 and 13-4-7-9.They might be equal.In this case the fake coin is either 3 or 8 because they are the only coins which were taken out of the system.
3AC.We just have to weigh 3 with another coin(besides 8)to see if that coin is equal to 3 or not.If it's not equal to 3,3's fake.If 3 is equal to another coin 3 is real.
1B.I really don't want to explain what happens if the other side is heavier because it's just the same thing all over again.Repeat the steps as if the other side was heavier etc. etc.
1C.What if they are equal?Then that means all these 8 are real and 5 are fake.We can put them like 9-10 to 11-12.That leaves out 13.
2CA.If 9-10 is heavier than 11-12 that means 13 is real.The others still might be fake.
3CA.For the last calculation we change 10 with 11 and 12 with 13.This makes the sides 9-11 to 10-13.13 is real and if the calculation gives 9-11 to be heavier that means 10 and 11 exchange didn't change anything and 9 is the heavier one and therefore the fake coin.If the pan says they are equal that means 12 is fake.Sadly I couldn't solve this part.What if the pan says 10-13 is heavier?That means either 10 or 11 could be fake and we can't know that without a 4th weihing.So I kinda mislead you and sorry for that.
2CB.Since I couldn't solve the problem no reason to repeat it :D
Sorry the post was very complicated I taught what the answer was maybe more then half an hour :D and right now it's 12:45 so please forgive me for writing it complicated-or atleast disorganised.If the posts can be edited I'm open to suggestions to make this mess a better text.And I will try not to post false answers again :D
Don't waste your time 
This is a very easy question to answer - The key is through reading comprehension as the statement says that the person can only go into the second room with the lamps one time. It never says how many times we can or can't go into the first room with the keys. So without further ade I will walk into the first room, take all 3 keys and proceed into the 2nd room one time to unlock the lamps. This problem is pathetically easy!!
Steinar's solution is good. Here's another explanation that might be easier to follow. Solved for 1 case Understand one case and working out the other cases is I think trivial.
We start with 13 unknowns and weigh 4 v 4 with 5 in reserve
trial 1 xxxx xxxx xxxxx (Right side -- bold pan-- goes down in all trials)
result LLLL HHHH GGGGG (L= possibly light H = possibly heavy G= known good)
trial 2 LHGG LHHG LLHGG
Result L HH GGGGGGGGGG
Trial 3 H H LGGGGGGGGGG
Result H! GGGGGGGGGGGG
There is one IQ test . If you want you can solve it and leave me message or post a topic here .
and we dont know which key is for which lamp . we can just one time go to the second room ( that room which the lamps are there )
# nobody can help you
# There arnt any windows in rooms
# You can not see the other room when you are in one of them
I guess grammar and basic English are not (arnt?) part of the IQ test.
OK, here's one:
There are two hills, side by side, with a stream that runs between.
On top of one hill is a tiny house, in which a woman and her very young daughter live.
One day, the house caught on fire, so the mother grabbed her daughter's hand and they ran out the door. They ran down the hill, crossed the stream and ran to the top of the other hill.
While sitting safely on the hill, looking across at their burning house, the young daughter said, "Thank God the three of us made it out of there."
what's going on?
----------------------
Across the street from our house are a lot of telephone lines. There are always lots of birds on those lines.
One day, we counted 96 birds. My brother then brought out his shotgun and fired one shot at a concentrated spot, instantly killing one half of one third.
How many birds were left?
For the second question, none -- birds don't stick around after a shotgun goes off.
For the second question, none -- birds don't stick around after a shotgun goes off.
So true - so correct.
what is one half of one plus one?
a. 1
b. 1.5
what is one half of one plus one?
a. 1
b. 1.5
1.5 -- order of operations
for the answer to be 1, it'd have to say what is one half of parentheses one plus one parentheses.
To be correct, 1/2*1+1 is not read the same as 1/2*(1+1)
correctomundo
i'm not going to bother with an IQ test given by someone who would write, "There are 2 rooms across from to each other ."
go away.
Macgyver would run as fast as he can for roughly 1 minute and 45 seconds to well past the half-way point of the bridge, then he'd turn around and run back toward the side he started on, until guardmar came out and saw him...that way guard sees that he is coming from the other side- in spite of originally starting on the same side - and then guardmar would throw MacGyver to the side he was coming from which is opposite the side he started.