Find top 5 horse from 25 horses

Question:

how to find top 5 horses from 25 if there are only 5 lanes.In min no. of races?

Red Marbles and Blue Marbles puzzle...goggle puzzle

Problem:

you have two jars, 50 red marbles, 50 blue marbles. you need to place all the marbles into the jars such that when you blindly pick one marble out of one jar, you maximize the chances that it will be red. (when picking, you’ll first randomly pick a jar, and then randomly pick a marble out of that jar) you can arrange the marbles however you like, but each marble must be in a jar.

Flying bird from trains puzzle(Bumblebee)

Question: 
Two trains enter a tunnel 200 miles long (yeah, its a big tunnel) travelling at 100 mph at the same time from opposite directions. as soon as they enter the tunnel a supersonic bee flying at 1000 mph starts from one train and heads toward the other one.
as soon as it reaches the other one it turns around and heads back toward the first, going back and forth between the trains until the trains collide in a fiery explosion in the middle of the tunnel (the bee survives). how far did the bee travel?

Daughters’ Ages

Question:
Two MIT math grads bump into each other at Fairway on the upper west side. They haven’t seen each other in over 20 years.

THE FIRST GRAD SAYS TO THE SECOND: “how have you been?”
SECOND: “great! i got married and i have three daughters now”
FIRST: “really? how old are they?”
SECOND: “well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..”

FIRST: “right, ok.. oh wait.. hmm, i still don’t know”
SECOND: “oh sorry, the oldest one just started to play the piano”
FIRST: “wonderful! my oldest is the same age!”

problem: how old are the daughters?

100 Doors in a Row...microsoft puzzle

Question:

you have 100 doors in a row that are all initially closed. you make 100 passes by the doors starting with the first door every time. the first time through you visit every door and toggle the door (if the door is closed, you open it, if its open, you close it). the second time you only visit every 2nd door (door #2, #4, #6). the third time, every 3rd door (door #3, #6, #9), etc, until you only visit the 100th door.

question: what state are the doors in after the last pass? which are open which are closed?

Solution:

For example, after the first pass every door is open. on the second pass you only visit the even doors (2,4,6,8…) so now the even doors are closed and the odd ones are opened. the third time through you will close door 3 (opened from the first pass), open door 6 (closed from the second pass), etc..

4 dogs chasing on corners of square

Puzzle:
There are four dogs, each at the counter of a large square. Each of the dogs begins chasing the dog 
clockwise from it. All of the dogs run at the same speed. All continously adjust their direction so that 
they are always heading straight towards their clockwise neighbor. How long does it take for the dogs to 
catch each other? Where does this happen? (Hint: Dog’s are moving in a symmetrical fashion, not along the edges of the square).

Enclosing land by fence pieces.(Microsoft puzzle)

Puzzle
You are given one 44-meter piece of fence and 48 one-meter pieces of fence.  Assume each piece is a straight and unbendable.  What is the large area of (flat) land that you can enclose using these fence pieces?

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Boat Ladder Puzzle

Puzzle

A boat has a ladder that has six rungs, each rung is one foot apart. The bottom rung is one foot from the water. The tide rises at 12 inches every 15 minutes. High tide peaks in one hour.
When the tide is at its highest, how many rungs are under water?


Solution
None, the boat rises with the tide.

Minimum no. of rats needed for finding poison in bottle....google puzzle

Question:
There are 8 bottles, one has poison. What's the minimum number of rats you need to find the poison bottle in time T, and how? (You get the rats you need all at once, feed them all at the same time, and poison kills them after time T.)


Solution:

representation in binary numbers
1-0001
2-0010
3-0011
4-0100

prove that n(n2-1) is div by 24...amazon puzzle

Question:

prove that n(n2-1) is div by 24

Note: n is odd and >=3

Solution:

N(N^2-1)=(N-1)N(N+1)
means it must be divisible by 2 and 3

since 24=2X2X2X3

Solution:Find average salary without knowing other`s salary

Solution:

Lets name these employees A, B, C and D

1. A chooses any random value and whispers it to B privately
2. B chooses any random value and whispers it to C privately
3. C chooses any random value and whispers it to D privately
4. D chooses any random value and whispers to to A privately

Find average salary without knowing other`s salary

Question:
How can four employees calculate the average of their salaries without knowing other's salary?