Copyright ©2014 by Paul Niquette. All rights reserved.
n the Differationale puzzle, solvers gasped upon reading this extraordinary passage...
asserts an infinity
kind of thing as it would pertain to a
particular puzzle kind of thing --
any puzzle that postulates a sequence of given
numbers and asks for one number -- the next
number in the series. The Differationale
demonstrated how the algorithm [a] takes into
account all of the given numbers without
regard to how they were created and [b] derives a
solution, which may or may not comply with what
the puzzle-master had in mind when creating the
puzzle, but [c] guarantees one and only one solution
-- complete with a rationale.
Here you are invited to consider the reverse of that challenge. In a Missing Numbers puzzle, only the first and last numbers in a series are given, and the solution comprises all the numbers in between. Solvers of the King for a Day puzzle will recognize that kind of thing...
...for which a linear interpolation algorithm would apply the fact that (666 - 1)/7 = 95...
...but we should note here that one and only one such solution will result from linear interpolation.
Nota bene, if the last number were, say, 667 instead of 666, (667 - 1)/7 = 95.14285~ we get...
...which would be an OK kind of thing if the puzzle-master allows for non-integer solutions.
onventional challenges authorize only integers for number sequences. Accordingly, linear interpolation will not always 'work'. Solvers will be able to show that a reverse version of the differationale algorithm will always 'work'. Let's call it the Missing Numbers algorithm.
Hey, and the Missing Numbers algorithm is not limited to one and only one solution. If you would like to figure out how that is possible, here is a question for you...
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