Question

To form 3 adjacent squares (as in the figure), 10 toothpicks are required. How many toothpicks are required to form 100 adjacent squares?

Answer 1

301

Answer 2

Let's say in general you want "n" adjacent squares. Each one needs a top, so that's n toothpicks. Each one needs a bottom, so that's another n toothpicks, and we're up to 2n total. You need one on the far left, and one on the far right, which brings us up to 2n + 2 toothpicks. Now we need to worry about the middle ones. But notice that you don't need n toothpicks for the interior because adjacent squares share. It turns out that you only need n-1. That brings us up to a grand total of 3n + 1 toothpicks, which would be 301 for n = 100.

Answer 3

220

Answer 4

I'm still lost, I might have to draw it out:(

Answer 5

I'll go with 301, and I'll let you know what the answer was.

Answer 6

Answer is 301

Answer 7

3n+1 where n is no of squares

Answer 8

Thanks Abdul

Answer 9

220 comes from forming a square arrangement, 10 by 10 of squares.