Solution:

Steps:
1) Light fire on first bar from both the ends and second bar from one end.

2) After 30 seconds(when first bar gets completely burned out) , burn the second bar from second end as well.

3) When second run completely gets burned , you know its 45 seconds.

Solution:

12:00

both minute and hour clock lie exactly between the number one and two in the number.

Solution:

12345679

12345679 × 9 = 111111111 (only 1s)
12345679 × 18 = 222222222 (only 2s)
12345679 × 27 = 333333333 (only 3s)
12345679 × 36 = 444444444 (only 4s)
12345679 × 45 = 555555555 (only 5s)

Solution:

Hhe hung herself using big Ice slabs , which are now now melted and hence puddle of water.

Solution:

1. We open the cupboard, put the dinosaur in the cupboard and close it.
2. We should open the cupboard, take the dinosaur out of cupboard, put the tiger in and close it.
3. The tiger, hes still in the cupboard
4. You swim across the lake as all the crocodile are at the party.

Solution:

2/3

While tossing the coins in this case only two cases are favorable:

1) A1 (H) A2 (H)

2) A2 (H) A1 (H)

3) B1 (H) B2 (T)

4) B2 (T) B1 (H)

Since the fourth case is not feasible, the probability is 2/3.

Solution:

45 minutes

Explanation :
All you have to do is burn the first rope from both the ends and the second rope from one end only simultaneously. The first rope will burn in 30 minutes (half of an hour since we burned from both sides) while the other rope would have burnt half. At this moment, light the second rope from the other end as well. Where, the second rope would have taken half an hour more to burn completely, it will take just 15 minutes as we have lit it from the other end too.

Thus you have successfully calculated 30+15 = 45 minutes with the help of the two given ropes.

Solution:

Jamie is a window cleaner who was tired after cleaning the windows on the 45th floor and thus leaped inside the building.

Solution:

Colors:
Y B R G
G R B Y
B Y G R
R G Y B


Signs:
x + - /
- / x +
/ - + x
+ x / -

Solution:

2