Suppose you had 8 billiard balls, and one of them was slightly heavier, but the only way to tell was by putting it on a scale against another. What’s the fewest number of times you’d have to use the scale to find the heavier ball?
There are three light bulbs in a room, and three light switches outside the room. You are outside, and want to match up which switch goes with which light bulb. You can only travel into the room once, and cannot come back in again. You can do anything you want upon entering the room. How can you set the situation so that you will know which switch goes with which light bulb?
Imagine an analog clock set to 12 o’clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs?
Imagine a disk spinning like a record player turn table. Half of the disk is black and the other is white. From the top-down the disc looks like a black and white cookie. Assume you have an unlimited number of color sensors. How many sensors would you have to place around the disk to determine the direction the disk is spinning? Where would they be placed?
Why is a manhole cover round?
A room contains a row of 100 light bulbs. Below each light bulb is a switch to control the bulb above. To begin, each bulb is off. You decide to pass through the row, flipping each light on, one-by-one. Your then make a second pass, this time flipping the switch for every 2nd light (#2, #4, #6…..#100), turning half of the lights off. You make a third pass toggling the switch for every 3rd light, then another pass toggling every 4th, then 5th, then 6th, all the way up to your 100th pass when you change the setting of only the 100th light.
How many bulbs are on after the 100th pass?
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Four From Five and Three
The Problem
If you had an infinite supply of water and a 5 quart and 3 quart pail, how would you measure exactly 4 quarts?