Math Riddle...?!


Question: If you place a chair 64 feet from a wall, then move it half the distance from where you were, closer to the wall (32 feet from the wall), then move it half the distance again (16 feet from the wall..etc....)....how many times will you have to move the chair until it is touching the wall? (Consider 2 times from 64 feet to 16 feet..and then add on the moves from there.) First to get it, gets 10 points.


Answers: If you place a chair 64 feet from a wall, then move it half the distance from where you were, closer to the wall (32 feet from the wall), then move it half the distance again (16 feet from the wall..etc....)....how many times will you have to move the chair until it is touching the wall? (Consider 2 times from 64 feet to 16 feet..and then add on the moves from there.) First to get it, gets 10 points.

It will never touch the wall, because you would always be going just half the distance

it would never touch the wall.

It would never touch the wall

In a math- only world, where infinitely small distances truly were possible, it would never touch the wall. However, in our world, where atoms begin interacting and can be said to be "touching" when they are an atom's width away, I would say that you will have to move the chair however many times until the gap is just an atom's width. If we take an atom to be about 50 pm wide, you would have to move your chair 39 times to be within that width.

moves 8 (8 feet from wall) moves 4 (4 feet from the wall) moves 2 feet (2 feet from the wall) moves 1 foot ( 1 foot from the wall) moves 1/2 a foot ( 1/2 a foot from the wall) moves 1/4 (1/4 from the wall) moves 1/8 ( 1/8 from the wall). Then it will be 0.875 feet in the wall. If it kept moving weather or not it was half way it would soon move 64 feet. So it did reach the wall. Thus making the chair move 9 times.

If it was a point in space, then everyone who answered NEVER is correct, as you we would always be dividing the distance between two points in half, which would be infinity. However, the chair does have a finite length. If one approximates an average chair of length 2 feet, then we need to calculate the number of times we can divide the distance until 2 feet is reached. I will assume the distance is measured from the center of the chair to the wall.

64
32
16
8
4
2
1 (half the length of the chair).

Thus, the chair, if moved 7 times, will touch the wall.

The above solution will not work if the distance is measured from the edge of the chair to the wall. In this case, the answer is NEVER.

You will never touch the wall because you will always have half the remaining distance to move the chair.

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