We connect dots with toothpicks in a grid as shown below. For example, the grid below has 7 horizontal toothpicks in each row and 5 vertical toothpicks in each column.

(a) Suppose we instead have a grid of dots that requires 10 horizontal toothpicks in each row and 20 vertical ones in each column. Then, how many total toothpicks will we need? Also, how many total dots are there?

(b) Can you generalize your answer? Suppose we have a grid that requires horizontal toothpicks in each row and vertical toothpicks in each column. Then, how many total toothpicks will we need? Also, how many total dots are there?

Please explain very well in this quesiton.

Guest Feb 27, 2015