Questions: Questions about …

The Most Intelligent Prince

A king wants his daughter to marry the smartest of 3 extremely intelligent young princes, and so the king’s wise men devised an intelligence test.

The princes are gathered into a room and seated, facing one another, and are shown 2 black hats and 3 white hats. They are blindfolded, and 1 hat is placed on each of their heads, with the remaining hats hidden in a different room.

The king tells them that the first prince to deduce the color of his hat without removing it or looking at it will marry his daughter. A wrong guess will mean death. The blindfolds are then removed.

You are one of the princes. You see 2 white hats on the other prince’s heads. After some time you realize that the other prince’s are unable to deduce the color of their hat, or are unwilling to guess. What color is your hat?

Note: You know that your competitors are very intelligent and want nothing more than to marry the princess. You also know that the king is a man of his word, and he has said that the test is a fair test of intelligence and bravery.

Electric Bulbs
Imagine you are in a room with 3 switches. In an adjacent room there are 3 bulbs (let’s say in electric lamps which are on a regular table) - all the bulbs are off at the moment, each switch belongs to one bulb. It is impossible to see from one room to another. How can you find out which switch belongs to which bulb, if you may enter the room with the bulbs only once?

Find out which switch belongs to which bulb - identify all 3 switches (so find out what bulbs are switches 1, 2 and 3 connected to)

Algebra Questions-1

This is first question in the series of Algebra Questions. The numerals in this question are replaced by letter codes. Replace the same characters by the same numerals so that the mathematical operations are correct.

CODED QUESTION

ABCB - DEFC = GAFB
      :         +         -
   DH x    AB  =    IEI
——————————
GGE  + DEBB = DHDG

In other words, find the parameters A, B, C, D, E, F, G, H, and I.

Hole in a Sphere
“Hole in a Sphere” question may be solved using calculus or more easily using logic.
A 6-inch hole is drilled through a sphere. What is the volume of the remaining portion of the sphere?
Clarifications:

1. the hole is a circular cylinder of empty space whose axis passes through the center of the sphere - just as a drill would make if you aimed the center of the drill at the center of the sphere and made sure you drilled all the way through.
2. the length of the hole [6 inches] is the height of the cylinder that forms the inside surface once the hole is drilled. picture the inside surface as viewed from inside the hole and measure the length of that surface in the direction of the axis of the drill.

in this sense, you could for example drill a 6-inch hole through the earth. the diameter of the hole would be huge, and you’d just have a tiny remnant of the earth left. but if you could set it on a table [a big table] it would be 6 inches high.
You of course could not drill a 6-inch hole through a sphere whose diameter was less than 6 inches. This fact leads to the logical answer.
The hard way involves calculus. The easy way uses logic.

The Man in the Elevator

“The Man in the Elevator” question is probably the best known and most celebrated of all lateral thinking logic puzzles. It is a true classic. Although there are many possible solutions which fit the initial conditions, only the canonical answer is truly satisfying.

The Man in the Elevator
A man lives on the tenth floor of a building. Every morning he takes the elevator down to the lobby and leaves the building. In the evening, he gets into the elevator, and, if there is someone else in the elevator - or if it was raining that day - he goes back to his floor directly. Otherwise, he goes to the seventh floor and walks up three flights of stairs to his apartment.
Question: How come?