The Mystery Of The Magic Grid
9 5 3 4 1 0 8 4 2 3 9 9 5 3 4 1 0 6 2 0 1 7 7 3 1 2 8
Pick 5 numbers on this 5 × 5 grid such that only 1 number appears in each column and row. Sum those 5 numbers. What is the result?
The answer is 25.
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2 solutions
So what am I doing wrong? In columns: 1 - 5 and 4, 3 - 4 4 - 2 5 - 2
= 17 I filled the requirements that no 2 numbers are adjacent. Other answers include 20. Never 25. Yet all my answers were rejected as incorrect.
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Oh, I interpreted the question as: "...such that no two numbers are in the same column or row." If it really is that no two can be adjacent, then this question is broken.
Sorry to everyone for poor phrasing. Don't know how I let it happen, I thought over it for a while.
You are limiting the condition to choose only those numbers who are in diagonal. Now all of those numbers diagonally, It will result 2 5
Actually, he/she is not limiting it to be in the same diagonal. Here I am wondering why this works, as there is total of 120 different ways to get the sum 25.
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Well , to give a tip. Consider the condition of selecting numbers such that they are all on different rows and in columns in a sequential manner firstly to establish an organized way of thinking. That is you can think some like " firstly , thinking just of columns , I have to select a number in every column such that all numbers selected from the columns stand on different rows". Then think of how for selecting this numbers their sum changes related to their increases and decreases anyway.
The problem does actually analyze exactly the behaveour of increase/decrease of the sum by selecting numbers such that they stand on different columns and rows. You can consider therefore their bigness and smallness (that is magnitude or size) of numbers to try to express exactly this way of behaving of the numbers in the square (sort of an inverse magic square) and as such anyway solve the puzzle/mystery by understanding the behaveour which makes the 120 ways work anyway.
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Relevant wiki: Mind Reading with Math
As is seen in this table, this grid is essentially an addition chart. No matter how you choose your numbers, you are going to end up with each of the numbers at the top (3 2 3 0 1) combined with the numbers on the side (6 2 0 1 7) in one way or another. So, your inevitable total is just (3 + 2 + 3 + 0 + 1) + (6 + 2 + 0 + 1 + 7) = 9 + 16 = 25