Math Puzzle
Difficulty: Medium
There is a square field of length ‘a’ (any positive real number) whose corners are A,B,C,D in the clockwise direction. Two persons started running from corners A and C along the circumference of the square field in the clockwise direction with integral speeds of v1 and v2.
Initially, at time t=0, distance between them is AC=√2a. Find the time t in terms of a, v1 and v2 when the distance between them is √2a for the next time.
Comments/Solutions are welcome.
Math and Logic Puzzle
Difficulty: Medium
There are 60 records given to you which correspond to a prisoner who is imprisoned for 60 days. He has 6 relatives of which one of them visits him daily and the others visit him every ith day from the day of his imprisonment (i=2,3,4,5,6 for these 5 relatives).
Every record is sealed with the day number on it which implies the number of days he is jailed when the record is filed with the names of visitors on that particular day. You have to make a new record which should be filled with the following details:
visitor name – number of visits after 1st 60 days
Assume that no other relatives visited him at all, names of these 6 relatives are different and you don’t know their names. Find the minimum number of records that need to be checked to make the new record correctly. Find the number of ways you can choose minimum number of records and still you can make the new record correctly.
Comments/Solutions are welcome.
Logic & Math Puzzle
Difficulty: Medium
There are two rooms A and B which are not connected and whose entrances are closed. Each of the rooms has 5 bulbs inside the room and 10 switches outside the room corresponding to bulbs of both the rooms.
The entrances will stay opened if and only if exactly one of the switches outside A and one of the switches outside B are ON. If both the switches that are turned ON correspond to the same bulb then the bulb will be OFF.
You are asked to find the bulbs corresponding to each of the switches outside rooms A and B. Using optimal methods, find the minimum and maximum number of trials required to complete the task.
Note: A trial is defined as turning one of the switches outside A and one of the switches outside B ON and checking the bulbs in the rooms A and B. There is no way to find which bulbs are ON from outside the rooms. The bulbs are at a reasonable height so that you can’t touch any of them.
Bonus:Assume that you are choosing both the switches(one from A and one from B) randomly i.e., not using optimal methods, find the probability that the task is completed in minimum number of trials.
Comments/Solutions are Welcome.
PS: I will be giving one puzzle everyday from today. Enjoy solving the puzzles.
