1 - Measuring 45 minutes with two ropes and a lighter.
Set fire to rope A at both ends, and rope B at one end. When the two burning ends of rope A meet, 30 minutes have passed. At this point set fire to the other end of rope B. When the two burning ends of rope B meet, a further 15 minutes have passed. Total elapsed time, 45 minutes.
2 - Heads and tails
3 - Farmer, fox, hen and corn
Take the hen over, leaving the fox with the corn. Take the fox over but bring the hen back again. Drop the hen off in its original place and bring the corn over. Leave the fox with the corn and go back to get the hen.
(I didn't work this out, it's an old one)
4 - Making a chain loop
3 cuts. Take one of the short chains and break it into its 3 component links. Use these 3 links to join the other three chains into a loop.
5 - Probability of having two daughters
I have seen this answered as 33%, but the real answer is 50%. There are four possibilities (she has an elder sister, a younger sister, an elder brother or a younger brother) in two of these 4 possibilities, the family has two daughters, so the probability is 50%.
6 - Blue and red jelly beans.
Take one bean from the box marked 'red and blue'. If the bean is red, then that is the box holding only red beans, the box marked 'red' has blue beans, and the box marked 'blue' has red and blue. (and reverse - If the bean is blue then the box marked 'red and blue' holds all blue beans, the box marked 'blue' holds red, and the box marked red holds red and blue).
7 - When ice melts does the water rise
The water stays at the same level. Ice displaces the same mass of water that it melts into. (Global warming raises sea level because some of the melting ice isn't currently displacing water, it's on land).
8 - finding the counterfeit among 8 coins with two weighs
Put two coins aside and weigh the remaining six, three against three.
If they balance exactly, the counterfeit is in the two you set aside - weigh them against each other to see which is heaviest.
But if one group of three coins is heavier, use that for the next test. Set one aside, and weigh the remaining two. If one is heavier it is the counterfeit. If they are the same, the one you set aside is the counterfeit.
9 - Water into wine
You have diluted the wine with pure water, but you have diluted the water with 'wine and water'. So there is more water in the wine than there is wine in the water.
10 - Crossing the bridge
The fast walker holds the torch. He crosses slowly with each person in turn, and then runs back quickly to get the next one. So the time taken is 5+1+4+1+3+1+2 = 17 minutes.
11 - Going south and east and north.
I can't do this one.
12 - How old are the daughters
My guess is that the house number is 14, meaning the 3 daughters could be twins of 6 plus a two year old (6*6*2=72, 6+6+2=14) or twins of 3 plus an eight year old (3*3*8=72, 3+3+8=14).
When the father says 'My eldest daughter likes shortcake' he is telling you that he has one elder daughter and two younger twins, so the second answer is right.
However, this is nonsense, as even with twins you have an 'elder' one. Humph.
13 - Planes going round the world
Despite instant refuelling, I think you need three support planes plus the round the world plane.
With an in-flight refuel at 1/6 of the way round, he can get 2/3 of the way round the world before he runs out, and at that point he can meet a refuelled support plane coming the other way round the world to meet him with enough spare fuel to get both planes another 1/6 of the way back to base. At that point they are met by two further support planes which refuel them both enough to get home.
14 - which switch controls the light.
Turn on switches A and B. Wait a minute and turn off switch B. Now go and check the bulb.
If the bulb is lit, A is the right switch. If the bulb is dark but hot, B is the right switch. If the bulb is cold, C is the right switch.
15 - wine again?
Isn't this the same as question 9? Not sure if that's the test.