Can you place every number from 1 to 9 into a 3×3 grid such that the range of every row and column is a unique value? The range of a row is the difference between its maximum and minimum values (similarly for columns). Good luck!
What does ABCD mean on a 4×4 grid?
The total sum remains the same as the sum of the diagonal. Here’s another way to think about it. Write abcd to mean in row 1 the number is in column a, in row 2 the number is in column b, in row 3 the number is in column c, and in row 4 the number is in column d. For example, 1234 means the diagonal with numbers 1, 6, 11, and 16.
How is the sum of 4 numbers in a grid always the same?
= 34. And that’s how the trick works: the sum of 4 numbers in this grid, each in different rows and different columns, is always the same as the sum of the numbers in the diagonal, which is 34. Source:
What is the range of a row in math?
The range of a row is the difference between its maximum and minimum values (similarly for columns). Good luck! first placing the 1 and 9 in one row, to get the largest range. The next numbers I placed were 2, 8, 3, 7, 4, 6, 5. In other words I worked from the outside (largest/smallest) inwards.
How to find the median of a row?
Each row will have one element that’s closest to the overall median from the left and one from the right (or be missing one of those). Since each row is sorted, we can use binary search. Testing how close an element is to the median requires O (n log m) comparisons, and we’d need O (n * log m) such tests.
Why are there only 3×3 magic squares in Excel?
The reason there are only these 3×3 magic squares is simple enough. Each row must add up to 45 / 3, that is, 15. Next, if you add the two diagonals and the middle column, you’ll get 15+15+15=45 again.
How to find median in a whole matrix?
For finding in the whole matrix, the complexity is N*log M with binary search. Then first find the minimum and maximum element from the N*M matrix. Apply Binary Search on that range and run the above function for each x. If the number of elements in matrix ≤ x is 1 + N*M/2 and x contains in that matrix then x is the median.
