1. Pencils and Jars
I have some pencils and some jars.
If I put 4 pencils into each jar I will have one jar left over.
If I put 3 pencils into each jar I will have one pencil left over.
How many pencils and how many jars?
Ans: Let there be P pencils and J jars. Then this puzzle is easiest solved by writing two equations for the two unknown quantities, P and J.  How do we do this? The first line says that if you take bunches of 4 pencils each (that is, P/4), it will fill (J-1) jars, with one jar lef over. So P/4=J-1, or we can multiply through by 4 to get P=4J-4.  The second line says that if I leave over one pencil, and make the remaining pencils into bunches of 3 each, I will exactly fill all the jars, so (P-1)/3=J or P-1=3J, or further re-arranging, P=3J+1. Now the first equation said P=4J-4, the second says P=3J+1. Since the left sides of both equations are the same, we must have the right sides to be the same, or 4J-4=3J+1, or J=5. From here, and using either of the two equations, we get P=16.
      
2. Tower of Hanoi
The object of the game is to move all the disks one by one, from Tower 1 over to Tower 3, using the second tower as a temporary space. But you cannot place a larger disk onto a smaller disk. 
If you have a kid sister or brother, by all means borrow their toy! Or
else make one yourself with lids of different sizes (you don't really
need the central stick).
Ans: Let us call the discs D1, D2, D3 (see figure). Then first move D1 to the tower T3. Then, in order, we make the following moves: D2 to T2, D1 o T2, D3 to T3, D1 to T1, D2 to T3, D1 to T3, so the discs move to tower T3 in 7 moves.
If you can find a larger tower, by all means try with more discs. If you look at the web-page, https://en.wikipedia.org/wiki/Tower_of_Hanoi, you will find animated solutions for 3, 4, and even 6 disc towers! As well as the story behind this puzzle.

3. Census taker
A census taker approaches a house and asks the woman who answers the door, "How many children do you have, and what are their ages?"
The woman replies "I have three children, the product of their ages is 36, the sum of their ages is equal to the address of the house next door."
The census taker walks next door, comes back and says "I need more information."
The woman replies "I have to go, my oldest child is sleeping upstairs."
The census taker then says "Thank you, I now have everything I need."
What are the ages of the children?
Ans:
First off, you have to find all the possible combinations that multiply out to 36, and find the sums of these possible ages. The list is 
1x1x36=36, Sum=38
1x2x18=36, Sum=21
1x3x12=36, Sum=16
1x6x6=36, Sum=13
2x2x9=36, Sum=13
2x3x6=36, Sum=11
3x3x4=36, Sum=10
Now the census taker went to the next house. If the house number had been anything but 13, he would have found out the combination which adds up to that number. But he came back for more information, which means he could not figure it out. Hence the house number must have been 13, since there are two combinations whose ages add up to 13: (1,6,6) and (2,2,9).  But the lady then mentions her "oldest child". This means it is (2,2,9) because the other combination has two oldest children. The census taker doesn't need any more information!  The reason the census taker could not figure out the children's ages is because, even with knowing the number on the house next door, there were still two possibilities.
The only way that the product could be 36 and still leave two possibilities is when the sum equals 13. These possibilities being 9, 2 and 2 and 6, 6 and 1.
When the home owner stated that her "oldest" child is sleeping she was giving ths census taker the fact that there is an "oldest".
So the children's ages are 9, 2 and 2.
Source: www.mathsisfun.com