# When and where was the first logic-grid-based puzzle published?

Logic puzzles with a set of conditions and a "logic grid" are very popular. More than one publisher is currently producing puzzle books with these types of puzzles.

A Wikipedia article claims Charles Lutwidge Dodgson, (Lewis Carroll, author of Alice's Adventures in Wonderland.) was the instigator of what later became these type of puzzles.

When and where was the first logic puzzle using a logic grid published? Here is an example of a logic grid from Wikipedia: • Hmm... many puzzles not designed for a logic grid could potentially have been solved with one. Do you mean to ask about puzzles solved specifically using a logic grid, or puzzles which have the capacity to be?
– user20
May 21, 2014 at 23:27
• @Emrakul, "puzzles solved specifically using a logic grid", I am assuming the capacity developed then the use. But no reason not to answer both if you can do it. May 21, 2014 at 23:36
• Actually, believe it or not, logic grids are one approach among many to solve this class of reduction puzzles, which is why I ask. Though, I suppose it's true - we could just let the answers come in. I can't answer myself, though.
– user20
May 21, 2014 at 23:37
• Also see puzzling.stackexchange.com/q/89
– SQB
May 23, 2014 at 11:13

So while not explicitly a logic grid, Carrol's book The Game Of Logic popularized logic "puzzles" of this nature (his weren't exactly puzzles so much as complicated logical statements) with answers represented in a notational style of his own creation involving squares and counters.

These problems were later refined in magazines and articles into the modern variety of what we call the logic puzzle: a single unique combination of facts which could be deduced through a provided set of statements. These became increasingly common during the 1940s and 1950s. When printed in magazines, some would suggest the form of an array or grid to assist with the problem.

The first actual printed grid I can find is in Clarence Raymond Wylie, Jr's 1957 publication 101 Puzzles in Thought and Logic.

The sort of logic puzzles James Jenkins refers to involve n-valued logic where n is always at least 3, and, in my experience, almost always at least 4. The grid in James Jenkins's OP is for a problem in 4-valued logic.

By contrast, the logic problems Lewis Carroll invented are all in Boolean or 2-valued logic. His main work on the subject is Symbolic Logic (pub. 1896). His The Game of Logic (pub. 1886) has a narrower focus, namely syllogisms, where a conclusion is to be deduced from two premisses. Three boolean variables (x, y and m, in Carroll's notation) are involved. One premiss involves x and m; the other, y and m; a conclusion in x and y is to be deduced. For example:

• No exciting books suit feverish patients;
• Unexciting books make one drowsy.
• Therefore, No books suit feverish patients, except such as make one drowsy.

(question 13, p.52 & p.74)

In Symbolic Logic, Carroll progresses from the syllogism to the sorites, which has n premisses involving a total of n+1 variables. As before, the variables are Boolean and each premiss involves two of them. A sorites is really a chain of syllogisms.

It is true that Carroll taught how to solve his logic problems using diagrams. But these diagrams were not like the grid in the OP. They were like Venn diagrams in purpose, but using rectangles instead of curves. In Symbolic Logic, Appendix, section 6, p.174, Carroll mentions Venn's method of diagrams, and reproduces the designs which Venn suggests, for up to 5 variables. Carroll presents his own diagrams for up to 8 variables in section 7 of the Appendix, p.176-179.

Carroll's Symbolic Logic is just Part I (Elementary) of what Carroll planned as a three-part work. He worked on Part II (Advanced), but did not complete it, as he died in January 1898, slightly more than one year after Part I was published. But in Symbolic Logic, Appendix, section 10 (p.185-194), he gives 8 problems "as a taste of what is coming in Part II". Each of these has the nature of a 3-SAT problem, except that a conclusion is to be deduced (whereas in 3-SAT the task is merely to find out whether or not the premisses can all be satisfied), and some of the premisses involve four variables, not three. Each of these problems is in Boolean logic, except number 1, which is in three-valued logic. That problem is on Google Books here: Problem 1.

Though Carroll did not complete Part II, a lot of manuscripts for his work on Part II survive, and an incomplete version of Part II, edited by William Warren Bartley III, was published by Harvester Press in 1977 (ISBN 0-85527-974-5). This shows Carroll's methods for solving his logic problems, one method using trees and one using symbols. There is nothing like the grids in the OP, or even Carroll's diagrams mentioned above.

• Fascinating, great job! May 25, 2016 at 15:39