Three different one-digit positive intergers are placed in a bottom row of cells. Numbers in adjacent cells are added and the sum is placed in the cell above them. In the second row, continue the same process to obtain a number in the top cell. What is the difference between the largest and smallest numbers possible in the top cells? Also what is positive in tergers?
To solve this problem, let's start by understanding the process described.
We are given a bottom row with three one-digit positive integers. Let's assume these integers are a, b, and c.
In the row above, the adjacent cells are added, resulting in two sums: a+b and b+c. These sums are placed in the cells above them.
In the top cell, the adjacent cells are added, resulting in a final sum: (a+b) + (b+c) = 2a + 2b + c.
So the top cell value will depend on the values of a, b, and c.
To find the difference between the largest and smallest numbers possible in the top cells, we need to determine the maximum and minimum values of 2a + 2b + c.
Since a, b, and c are one-digit positive integers, the maximum value occurs when a, b, and c are the largest possible one-digit positive integers, which are 9, 8, and 7, respectively. In this case, the top cell value would be 2(9) + 2(8) + 7 = 43.
Similarly, the minimum value occurs when a, b, and c are the smallest possible one-digit positive integers, which are 1, 2, and 3, respectively. In this case, the top cell value would be 2(1) + 2(2) + 3 = 10.
Therefore, the difference between the largest and smallest numbers possible in the top cells is 43 - 10 = 33.
Now, let's address the second part of the question: "Also, what is positive integers?"
Positive integers are whole numbers greater than zero. In this case, it refers to the one-digit numbers (1, 2, 3, 4, 5, 6, 7, 8, 9) used in the bottom row of cells.