# Assumption Needed when Solving Puzzle

When solving a logic puzzle, at times, one must make an assumption in order for a solution to be found. For example, in this perfectly good logic puzzle, it had to be assumed that the characters knew amongst themselves who's who (i.e. the Knight knows who the Joker and Knave are, etc).

What is the technical term (a noun) which represents a necessary assumption, without which, a solution may be impossible? I have heard this term at some point (somewhere here on Puzzling.SE), but it has escaped me — if it helps, I think it was something like 'zero assumption' (90% sure it was more than one word) and it had a Wikipedia entry.

PS: I'm not entirely certain the puzzle I mentioned requires any extra assumptions - it's a perfectly good logic puzzle.

• @d'alar'cop I see. Is this a term particular to puzzles? If not, I think ELU is the place to go. – xnor Dec 5 '14 at 3:09
• @xnor Indeed, this is a dilemma I was facing... BUT the term is one of logic, and would only arise in solving puzzle where logic is a reasonable tool... but since it a term regardless, it may be the case. – d'alar'cop Dec 5 '14 at 3:12
• You might get an answer faster at EL&U, but I don't think there's any reason to consider this off-topic here. Technical terminology relevant to the site's material should definitely be a suitable question subject. – jscs Dec 5 '14 at 5:04
• @d'alar'cop Well in that case you can go wrong with both haha – For I In Range Dec 7 '14 at 14:18
• Is it not helpful to have incorrect guesses in comments remain posted so that others may know what the OP is not looking for? (I wasn't going to post speculative responses as proper Answers, myself.) – tjbtech Dec 7 '14 at 18:50

OP: Seems that it was: FIRST PRINCIPLE

Could it be Basic supposition? I've seen it in some (really old) books about philosophy and physics, but the full phrase does not have a Wikipedia entry.

EDIT

Scratch, that. You are probably searching for Tacit assumption, also known as Implicit assumption

SECOND EDIT

Could it be Unstated assumption as described in the second paragraph on the Wikipedia link?

THIRD EDIT (this is getting fun)

Or maybe First principle a.k.a. Foundational proposition/assumption

Bonus question: How many terms for practically the same thing are there?

• Not bad. I'm afraid that is not the term however. +1 for the hunt – d'alar'cop Dec 8 '14 at 13:44
• @d'alar'cop Even the one after the edit? – dmg Dec 8 '14 at 13:45
• Yes, even the edit :( – d'alar'cop Dec 8 '14 at 13:49
• @d'alar'cop Dang. This proves that SE Puzzling sucks at non-challenge questions :D – dmg Dec 8 '14 at 13:51
• LOL... well we need to get at this stuff too >:( – d'alar'cop Dec 8 '14 at 13:52

As someone with a little bit more of a math background, I call these assumptions constraints. The word comes from optimization, a field studied by both computer scientists and mathematicians. When you write a computer program to solve a problem like determining the most efficient way to schedule trains transporting materials, you provide the program constraints that limit what kinds of solutions are acceptable. For example, a weight limit on a train is a constraint, as is the fact that two trains can't go in opposite directions on the same tracks simultaneously.

Analogously, a basic assumption or constraint limits what solutions are possible in a puzzle.

Another word you might want to use to refer to the basic assumptions is givens. Again, this word is taken from math: When completing a mathematical proof, the ideas or objects that you're making a proof about are given to you at the start of the proof. For example, let's say you want to prove the Pythagorean Theorem: If a triangle is a right triangle with legs of length $a$ and $b$ and hypotenuse of length $c$, then $a^2+b^2=c^2$. The givens in this proof are that the triangle you are working with is a right triangle, and it has sides of length $a$, $b$, and $c$. If you take these details out, you don't have enough information to complete the proof!

Likewise, the assumptions you're allowed to make while solving a puzzle are the puzzle's givens. For example, in your problem about knights, knaves, and jokers, one of the givens is that the three characters know who each other are.

I don't think there's too much of a difference between a constraint and a given when discussing puzzles. If you want to be strict about it, though, a constraint is an aspect of a puzzle that puts requirements on an acceptable solution without decreasing the size of the search space (a hypothetical list of every possible solution based on a naïve reading of the puzzle), while a given is either necessary to ensure the puzzle can be solved or helps decrease the size of the search space. In other words, a constraint makes the puzzle harder by forcing you to find more complicated solutions, while a given makes a puzzle easier by pushing you in the right direction or ensuring a puzzle has only one provable answer. One can see where the difference can get blurry for a lot of puzzles.

• math FTW. I was thinking of another math-inspired answer like basis or base case – dmg Dec 8 '14 at 21:53
• hi Kevin, I'd say your argument about "givens" fits well with the term "first principle" in the other answer. please advise – d'alar'cop Dec 9 '14 at 1:00
• We can use terms from both our answers! Puzzling isn't formal, so as long as we get our ideas across, we can use whatever terms we want that effectively communicate our puzzles and their solutions. – Kevin Dec 9 '14 at 1:01
• @Kevin I absolutely agree. In many cases the so-called "reasoning" is simply applying formal logic to a well-defined mathematical problem. It is natural that maths can provide an answer to this question as well. – dmg Dec 9 '14 at 8:06

Could be axiomatic - an axiom.

An axiom or postulate is a premise or starting point of reasoning. As classically conceived, an axiom is a premise so evident as to be accepted as true without controversy. ... As used in modern logic, an axiom is simply a premise or starting point for reasoning.

https://en.m.wikipedia.org/wiki/Axiom