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The clue may require arithmetic to be applied to another answer or answers (e.g. "25 across times 3" or "9 down minus 3 across") The clue may indicate possible answers but make it impossible to give the correct one without using crosslights (e.g. "A prime number") One answer may be related to another in a non-determinate way (e.g.
Consider any primitive solution (x, y, z) to the equation x n + y n = z n. The terms in (x, y, z) cannot all be even, for then they would not be coprime; they could all be divided by two. If x n and y n are both even, z n would be even, so at least one of x n and y n are odd. The remaining addend is either even or odd; thus, the parities of the ...
Equivalent statement 1: x n + y n = z n, where integer n ≥ 3, has no non-trivial solutions x, y, z ∈ Z. The equivalence is clear if n is even. If n is odd and all three of x, y, z are negative, then we can replace x, y, z with −x, −y, −z to obtain a solution in N. If two of them are negative, it must be x and z or y and z.
The abbreviation is not always a short form of the word used in the clue. For example: "Knight" for N (the symbol used in chess notation) Taking this one stage further, the clue word can hint at the word or words to be abbreviated rather than giving the word itself. For example: "About" for C or CA (for "circa"), or RE.
The solver is given a grid and a list of words. To solve the puzzle correctly, the solver must find a solution that fits all of the available words into the grid. [1] [2] [8] [9] Generally, these words are listed by number of letters, and further alphabetically. [2] [8] Many times, one word is filled in for the solver to help them begin the ...
It is impossible to solve in half of the starting positions. [1] Five room puzzle – Cross each wall of a diagram exactly once with a continuous line. [2] MU puzzle – Transform the string MI to MU according to a set of rules. [3] Mutilated chessboard problem – Place 31 dominoes of size 2×1 on a chessboard with two opposite corners removed ...
Anacrostic may be the most accurate term used, and hence most common, as it is a portmanteau of anagram and acrostic, referencing the fact that the solution is an anagram of the clue answers, and the author of the quote is hidden in the clue answers acrostically.
One can divide by to obtain a differential equation of the form ″ + ′ + = which will not be solvable with regular power series methods if either p(z)/z or q(z)/z 2 is not analytic at z = 0. The Frobenius method enables one to create a power series solution to such a differential equation, provided that p(z) and q(z) are themselves analytic ...