Solution:

In this question, let us think through the mind of Lincoln. At the first information of the product of the ages being 72, he must have calculated the number of ways in which the three ages can be multiplied in order to obtain 72. Of course there are many ways and therefore he asked for more info. Then Michael tells him how to find the sum of the ages of his children. Of course, we don't know what he saw. But he said that the information was still not enough.

Now why did he say so? It is because there must be two permutations with the same sum or he would have identified the ages easily. Now what are those two permutations?

The two possible permutations are 8 3 3 and 6 6 2. Both of them adds up to 14 (which would be the bar's address).

The last hint by Michael was that his youngest child loves to eat strawberry ice cream. The term youngest means that there is only one youngest child. If you see the permutation 8 3 3, it will mean that there are two youngest children. Thus it does not stand valid with the third hint. So, we are only left with one possibility i.e. 6 6 2.

Thus the ages of his children are 6, 6 and 2.

Solution:

f the last elf is taking some time to answer the question then it shall mean that the elf's before him are all wearing distinct coloured hats. However sufficient time shall be given to the last elf to give the answer.
If he views the similar coloured hats in front of him , he shall quickly tell the answer

Solution:

Now there can be two solutions to the given situation because there can be two situations:
Suppose if B and C have same colors, A will know that his color is the other one and he will be able to speak up the first.
Now if B and C do not have same colors, A will stay silent. This will tell B that his and C's colors are different. Thus he will speak up first.

So either A or B will speak up first depending on the situation.

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:

5 leopard and one sheep

since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.

Solution:

12 steps:

Steps 11 Liter jug 6 Liter Jug
1. 11 -
2. 5 6
3. 5 0
4. 0 5
5. 11 5
6. 10 6
7. 10 0
8. 4 6
9. 4 0
10. 0 4
11. 11 4
12. 9 6 ==> i found 9 liter in 11liter jug(as required)

Solution:

Difference 1
Toy plane direction is different.

Difference 2
On the clock, number 1 & 2 is missing.

Difference 3
The colors of lamp's light is changed.

Difference 4
The ribbon on the gift is missing.

Difference 5
Duck is added in the gift section.

Solution:

There are 3 fruits (1 grapes, 1 apples, and 1 oranges).

Solution:

10

Explanation:
Equation 1 + 9 + 11 = 1 can be derived from
One (o) + nine (n) + eleven (e) = one => 1

Similarly for equation,
12 + 11 + 9
Twelve (t) + eleven (e) + nine (n) => ten (10)

Solution:

Four

As the window was closed it is obvious that the six candles that were not extinguished were lit till they melted away entirely. Thus only four candles that were extinguished remain at the end.

Solution:

Tilt the barrel until the fruit juice barely touches the lip of the barrel. If the bottom of the barrel is visible then it is less than half full.If the barrel bottom is still completely covered by the fruit juice, then it is more than half full.