Suppose you have twelve eggs and a balance scale. All of the eggs are identical except for one whose only difference is its weight. Using the scale only three times, determine which egg is the odd egg out and whether it is heavier or lighter than the other eggs.
Weigh four against four. If they’re equal, weigh three of them against three you haven’t weighed. If they balance too, weigh the last remaining egg against any of the others to see if it is lighter or heavier. If the three suspects are heavier, weigh one of them against another and the one that goes down is it. If they balance the remaining suspect is heavy. Use the same process if they’re lighter. If the initial four vs four don’t balance, weigh two heavy eggs and a light egg against one heavy egg, one light one and a known normal egg. If they balance weigh the remaining two light eggs against each other. If they balance the unweighed heavy egg is the odd one out. If the side with two heavy eggs goes down weigh them against each other. If they balance it is the light egg on the other side. If the other side goes down it is either because of one heavy egg on that side or because the one light egg on the other side is lighter than the rest. Weigh one of them against a known normal egg to determine which is true.
You are standing outside a closed door. On the other side of the door is a room that has three light bulbs in it. The room is completely sealed off from the outside. It has no windows and nothing can get in or out except through the door. On the outside of the room there are three light switches that control each of the respective light bulbs on the other side of the door.
Your assignment is to determine which light switch controls which light bulb. You are allowed to enter the room only once, and once you come out, you must be able to state with 100% certainty which light switch controls which light bulb.
Turn one light switch on, wait a few minutes, then turn it off and turn another light switch on. Go into the room and feel the light bulbs. The one that’s still warm is connected to the switch that you first turned on, the one that is on was the second switch you turned on, and the last bulb is controlled by the switch that you didn’t touch.
I have many feathers to help me fly. I have a body and head but I’m not alive. Your strength determines how far I go. You can hold me in your hand, but I’m never thrown.
A six-digit number represented by ABCDEF (each letter represents a different number) can be multiplied by 2, 3, 4, 5, and 6 and yet no new digits appear in the result. As a matter of fact, all the digits are rotated. What is the number?
Three travelers register at a hotel and are told that their rooms will cost $10 each so they pay $30. Later the clerk realizes that he made a mistake and should have only charged them $25. He gives a bellboy $5 to return to them but the bellboy is dishonest and gives them each only $1, keeping $2 for himself. So the men actually spent $27 and the bellboy kept $2. What happened to the other dollar of the original $30?
There is no missing dollar from the original $30 because after getting $1 back, the three travelers had paid a total of $27 for their room ($9 each), not $30. Out of that $27, the hotel has $25 and the clerk kept the remaining $2. If you still want to work from the original $30, the travelers have $3, the hotel has $25 and the bellboy has $2. The misleading part is adding the bellboy’s $2 to the $27, when in fact it should be subtracted.
The next number in the sequence is n squared minus m or f(n,m) = n2 – m
f(6,9) = 62 – 9 = 27
f(9,27) = 92 – 27 = 54
f(27,54) = 272 – 54 = 675
f(54,675) = 542 – 675 = 2241