How many ways can we arrange the numbers 1 through 9 in a 3x3 grid such that the following conditions hold?
- Every number is greater than the number directly above it.
- Every number is greater than the number immediately to the left of it.
There is only one way to do that:
Any number on top row cant be replaced with one from below or any number on left column cant be replaced with one from right to meet those two conditions.
Nine consecutive integers are placed in the nine squares of a 3x3 grid. If every column, every row, and every diagonal adds up to the same number n and the middle number is 8 what is n?
There are 12 different chocolates placed on a table along a straight line. In how many ways can a person choose 4 of them such that no 2 of the chosen chocolates lie next to each other?
6 boys and 7 girls are available for a counselling.
In how many ways, we can arrange them in a row, if middlest one is a boy and girls are sat on both the corners?