Puzzle 79 | Magical Matrix Last Updated : 18 Jan, 2023 Comments Improve Suggest changes Like Article Like Report Two friends Satyam and Ankit decides to play a game. They have 9 cards lying face up with numbers 1 to 9 written on them. They have to start picking up these cards alternately, without replacement. The person with exactly 3 cards which adds up to 15 wins the game. Satyam is given first chance to pick up a card . Does Satyam have a winning strategy? Solution: No Explanation: We see that there are eight subsets of {1,9} that sums up to 15. These are: {1, 5, 9}, {2, 8, 5}, {3, 5, 7}, {4, 5, 6}, {1, 6, 8}, {2, 4, 9}, {2, 7, 6} and {3, 8, 4} We can try to form a magic square which should be able to derive all possible combinations that sums up to 15. 8 1 6 3 5 7 4 9 2 Here we see each row , column or diagonals sums up to 15. These rows ,columns and diagonals represents all the possible ways the number fifteen can be arrived at. We can observe it's like playing a tic-tac-toe on the magic square. We also know one cannot guarantee winning in this game. At maximum, we can have strategy of not losing the game. This puzzle is contributed by Ankur Chaudhary. Comment More infoAdvertise with us Next Article Puzzle 79 | Magical Matrix K kartik Follow Improve Article Tags : Aptitude Arrangement Puzzles Similar Reads Puzzle 84 | Inverted Matrix You have been given the following matrix: Fill in the matrix, in such a way that the sum of the numbers in each row (horizontally, vertically, and diagonally) is 264, even if you hold the matrix upside down. You are only allowed to use the digits 1, 6, 8, and 9, and each number may appear only once 1 min read Coxeter method to construct the magic square Given an odd integer N, the task is to find the magic square of order N. Examples: Input: N = 3 Output: 6 1 8 7 5 3 2 9 4Input: N = 5 Output: 15 8 1 24 17 16 14 7 5 23 22 20 13 6 4 3 21 19 12 10 9 2 25 18 11 Approach Put the value 1 in the middle of the first row. Let the position be (i, j). Now mov 8 min read Magic Squares: Fun Fact and More Magic squares are intriguing numerical forms that have always drawn the keen interest of mathematicians as well as problem-solvers of all age groups. They are interesting mathematical sequences of figures that have the property that the sum of the figures in any row and any column as well as the sum 8 min read Magic Square | Even Order A magic square of order n is an arrangement of n^2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A magic square contains the integers from 1 to n^2.The constant sum in every row, column and diagonal is 13 min read Magical Pattern Given an integer N as input, the task is to print the Magical Pattern as given below: N . . 3 2 1 2 3 . . N . . . . . . . . . . . 3 3 3 3 2 1 2 3 3 3 3 2 2 2 2 2 1 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 1 2 2 2 2 2 3 3 3 3 2 1 2 3 3 3 3 . . . . . . . . . . . N . . 3 2 1 2 3 . . N Examples: Input: 9 min read Like