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The Sum and Product Puzzle, also known as the Impossible Puzzle because it seems to lack sufficient information for a solution, is a logic puzzle. It was first published in 1969 by Hans Freudenthal, [1] [2] and the name Impossible Puzzle was coined by Martin Gardner. [3] The puzzle is solvable, though not easily.
Cheryl: I have two younger brothers. The product of all our ages (i.e. my age and the ages of my two brothers) is 144, assuming that we use whole numbers for our ages. Albert: We still don't know your age. What other hints can you give us? Cheryl: The sum of all our ages is the bus number of this bus that we are on.
The Ages of Three Children puzzle (sometimes referred to as the Census-Taker Problem [1]) is a logical puzzle in number theory which on first inspection seems to have insufficient information to solve. However, with closer examination and persistence by the solver, the question reveals its hidden mathematical clues, especially when the solver ...
Sudoku solving algorithms. A typical Sudoku puzzle. A standard Sudoku contains 81 cells, in a 9×9 grid, and has 9 boxes, each box being the intersection of the first, middle, or last 3 rows, and the first, middle, or last 3 columns. Each cell may contain a number from one to nine, and each number can only occur once in each row, column, and box.
2 Explanation of the puzzle. 2 comments. 3 The sum of x and y is 100 or less. 1 comment. 4 I hesitate to add another program. ... Talk: Sum and Product Puzzle.
Product (mathematics) In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors. For example, 21 is the product of 3 and 7 (the result of multiplication), and is the product of and (indicating that the two factors should be multiplied together).
In arithmetic combinatorics, the Erdős–Szemerédi theorem states that for every finite set of integers, at least one of , the set of pairwise sums or , the set of pairwise products form a significantly larger set. More precisely, the Erdős–Szemerédi theorem states that there exist positive constants c and such that for any non-empty set.
A sum-product number in a given number base is a natural number that is equal to the product of the sum of its digits and the product of its digits. There are a finite number of sum-product numbers in any given base . In base 10, there are exactly four sum-product numbers (sequence A038369 in the OEIS ): 0, 1, 135, and 144.