A certain ball, when dropped from any height, bounces one-third of the original height. If the ball is dropped from 54 metres, bounces back up, and continues to bounce up and down, what is the total distance that the ball has travelled when it hits the ground for the fourth time.
Arstil and Byzinte are two neighboring islands in a far-off corner of the world. The natives of Arstil (the Arstilians) and the natives of Byzinte (the Byzintians) sometimes visit each other's island. Their strange thing is that whenever the islanders are on their home island, they tell the truth, but whenever they are on the other island, they lie.
One day an explorer landed on one of the islands, but didn't know which one. She then met two islanders, but didn't know whether they were from the same island or not. One of them said: "We are from different islands". Then the explorer asked: What island are we now on?" The other replied: "Arstil". The explorer then knew which island she was on. Which island was it?
A system of switches A, B, C and D control a set of four lights. When each switch is working, it has the following effects on the lights:
Switch A turns lights 1 and 2 on/off or off/on
Switch B turns lights 2 and 4 on/off or off/on
Switch C turns lights 1 and 3 on/off or off/on
Switch D turns lights 3 and 4 on/off or off/on
In the following diagram, switches C B D A are thrown in turn, with the result that Figure 1 is transformed into Figure 2. Therefore, one of the switches is not working and has had no effect on the numbered lights.
A rotating Gear X in a diesel engine revolves around two fixed Gears Y and looks like this. ALL three gears are indentical in size. How many revolutions will Gear X make in one full rotation around the fixed gears?