Post a mathematical riddle
MA375, Spring 2010, Prof. Walther
- Come up with an algorithm that counts down from a number but does not employ the use of a minus sign or any form of subtraction. There are several solutions to this problem.
- How can you add eight 8's to get the number 1,000? (only use addition)
(TQU: 888+88+8+8+8 = 1,000)
- Start with six vertical lines. Then add 5 more lines to make nine.
- Find the pattern: 8, 11, 15, 5, 4, 19, 7, 6, 3, 22, 2
- If an analog clock shows the time 4:30, what is the angle between the hour and minute hand?
(BD: Angle covered by each hour = 360deg/12hour = 30 degrees/hour. At 4:30, hour hand is halfway between 4 and 5, and minute is at 6--so, 30 deg between 5 and 6, and an additional 15 between 4.5 and 5 = 45 degrees.)
- Assume you are in need of a way to accurately weigh objects, but all you have is a simple scale and a 40 pound rock. There is a rockcutter in a nearby town who can very accurately cut the rock into pieces of whatever weight you want. How many pieces, and of what weights, do you ask the rock to be cut into in order to be able to measure the weight of any object up to 40 pounds? Bear in mind that the rockcutter charges by the cut, so it is in your interest to ask for the minimum number of pieces you need. (Also, you can assume every object you will be weighing has a weight which is an integer number of pounds.)
This is one of those very interesting riddles which is asked rather often at interviews for consulting companies and what not. The question asks in how many weighings(using a balance i.e. you can only see if one side is heavier of lighter) it is possible to find a defective ball(heavier or lighter) from a set of 8 balls. The next part is to generalize the solution.
