What is this kind of reasoning called?

[dstebbins]

I've seen it played numerous times in the Clock Game. The goal is when you are faced with a ton of possibilities, and you try to eliminate as many possibilities as you can, so that you are left with only one possible answer. This can make the Clock Game easy to win, even if you have no earthly idea what the price of the item is.

 

"five hundred"

"Higher."

"seven fifty"

"Higher"

"Nine hundred"

"Lower"

"Eight hundred"

"Higher"

"Eight fifty"

"Higher"

"Eight eighty"

"Higher"

"Eight ninety"

"Higher"

"91, 92, 93, 94, 95, 96, 97, 98, 99-"

"THAT'S IT!"

 

The fridge is worth $899.

 

The Clock Game is the most common example, but not the only one, where this strategy is definitive.

 

What is called?

[Mr Skeptic]

Well that's just inefficient.

 

A better way is a binary search

[TonyMcC]

If you know a value that must be higher than the maximum possible and another value which is lower than minimum possible then a system known as the Half Split Technique is efficient. It is often used for isolating faults in complex systems. Google "Half Split Technique" for further info.

[ewmon]

What is called?

It's called a search algorithm, and we do it every time we open a book, most obviously, a dictionary, but also textbooks. Flipping pages is an extremely simple yet inefficient algorithm, and your example shows "flipping pages" only at the end where the possibilities have dwindled to a handful.

 

With electronic systems, binary searches are used, and I've also read where the Golden Ratio (using 0.618033... instead of 0.5 in binary searches) can be more efficient. Generally speaking, there's also various methods such as hash functions and sorting algorithms used for categorizing/sorting/storing/searching for data. Alphabetization is a very common sorting algorithm, classically used in dictionaries, filing cabinets, computers (lists of file names), etc.

 

I wonder if using the Golden Ratio improves efficiency due to Benford's Law.

Edited September 30, 2010 by ewmon