Puzzles

  I have yet to see any problem, however complicated, which, when looked
at in the right way, did not become still more complicated.
                -- Poul Anderson
 

1. Wire encoding:    There is a cable with 55 wires in it laid across a river. All you have is a multimeter (a device that can measure resistance, voltage and current) and wires of multimeter are not long enough that you can connect two terminals across the river. You have to establish a one-to-one correspondence between the ends of all the 55 wires. How can you do it in minimum number of crossing of river ?
2. 500 doors: There are 500 doors in a row, all closed. 500 men pass by these doors and i-th person toggles the position of every i-th door( for example 3rd person toggles door no. 3,6,9.....). At the end, how many doors are open ?
3. Playing with adversary: There is a small  dark room with 4 switches in 4 directions at 90 degree apart (north, south, east and west). The doors of room will open only when all the switches are up or all are down. You are standing on a platform which can be rotated by an adversary. You can extend your arms and feel position of any two switches and change their position but as soon as you do it, the adversary turns the platform by some integer multiple of 90 degrees. Initially the switches can be in any position. How can you get out of room ?
4. 62 Squares: There is a square board of 8x8 size and two squares of size 1x1 are cut from diagonally opposite corners of the board. You have rectangles of 2x1 sizes and have to cover the board with these rectangles such that they cover all the area and they never overlap each other or extend beyond the board. How can you do it ?
5. Linked list with loop: There is a singly linked list such that the last element of list may point to null or point to one of the elements in the list itself. All you have is memory for three pointers. How can you non-destructively figure out if the list terminates at null or the last element points to one of the elements in the list in finite time ?
6. High-school geometry 1: You are given a rectangle drawn on a paper. All you have is a compass and a ruler. How can you draw a square of area same as that of given rectangle ?
7. High-school geometry 2: How  do u make 4 triangles with 6 match sticks each of same lengths so that the sticks do not cross each other( only the ends of sticks can touch each other)
8. Cool light bulbs: There are 3 light bulbs in a room and 3 switches outside each corresponding to a bulb such that you can not see anything in the room if you are operating switches. You can do whatever with the switches and then you are allowed to go in the room only once. You have to figure out which switch corresponds to which bulb.
9. Dumb robots: There is an infinite straight line on which two robots are dropped at random positions. They land with a parachute and put their chute where they land and then start executing a code that you have to provide. Both robots land at same time and start executing the same code. The instruction set has only 4 instructions. Move left one step, Move right one step, If (cond) goto line no(x), No-op. Left and right is predefined for both the robots (i.e., both of them consider same direction as left). You have to make the robots meet each other in finite time by loading a finite amount of code.
10. Fragile balls: You have two identical balls and a hundred-floor building. There is an integer F such that either ball will break if dropped from F or higher floor. How can you determine F in minimum number of drops? If you start testing balls from ground floor, it may take 100 drops. If you think a little more you can improve it to 19. What is the strategy that minimizes the number of drops in worst case ( it is less than 19)?

"The first principle is that you must not fool yourself and you're the easiest person to fool." 

-- Richard Feynman