Step by Step

Logic Level 1

A man is 20 metres away from a door.

With every step he takes he covers half the distance between the door and himself.

In how many step will he reach the door?

Assume he can take a step of any distance.

Image Credit: Flickr Ximo Michavila .

2 4 5 He will never reach

4 solutions

Naman Mittal
Apr 23, 2015

He will never reach. Half of 20 is 10 then 5 then 2.5 then 1.25 then 0.62 and then on and on so mathematically the distance will never be zero

Mathematics vs Physics, Mathematics says you will never reach the door, Physics says after 5 steps you'll be close enough to open, shut, knock or do whatever you want with the door

AAron Grove - 5 years, 7 months ago

mathematically the distance can never be zero..well then rephrase the question and speak about a point!!!!its practically impossible ...even the limit to which the distance to the door can be measured is not specified...?

Sanjana Sebastian - 5 years, 8 months ago

Xeno's paradox...!!!

Rifat Ahmed - 5 years, 8 months ago

Princess Patricia Torres
Sep 4, 2015

Well the man is walking 20 meters AWAY from the door so it's only logical that he will never reach it.

The man is not walking away. Read the question properly

Naman Mittal - 5 years, 8 months ago

Nice spot, and there is no suggestion of that the distance covered is moved in the direction towards the door, or that it decreases each time. This disproves any of the theories surrounding that he would be able to reach the door with his arm or other means, or that on the infinite step he will reach it. Besides, nice find.

Luke Daly - 5 years, 8 months ago

Sergio Alejandro Acelas Avila
Apr 26, 2015

This is wrong, is the paradox of Arquimides, its prove that in certain moment the Man reach the door. Sorry for my horrible english, I am Colombian

The man will obviously reach the door if u think practically but if u try to get the answer mathematically then u see ur answer will never come to zero

Naman Mittal - 6 years, 1 month ago

if he takes infinitely step, then the distance should be 0,0000000000.......... and it still goes on, definitely it will be so close to 0

what do you think? will he reach the door? or never?

*theoretically

Moh Rahmanda - 6 years, 1 month ago

Yes the man will reach the door when he takes the infinith step (theoretically) so sorry the option should be infinity not never reach

Naman Mittal - 6 years, 1 month ago

@Naman Mittal – Mathematically he will never reach the door but after 5 steps he will be .625 Meters = 2.05052493 Feet from the door at which point he can reach the door without being 0 feet from it. Do you have to press your face against it to open it? After 5 steps his arm can reach it(assuming he isn't like 3 feet tall) even if he's a bit below average say 5 foot 6, his arm would still be more than 2 feet long.

Paul Willey - 5 years, 9 months ago

Eddie Spagnoli
Sep 22, 2015

The man will actually reach the door. He is walking toward the door, and since the man is not stated to have lost his arms, it can be assumed he does have them. He will come so close to the door within a few steps that he can reach is arm out and grasp the handle, thereby reaching the door.

The idea that he will never reach is due to Archimedes Paradox, where he will come so close to the door that it seems he is there, but will never arrive based on mathematics. I, however, am using logic...

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Image Credit: Flickr Ximo Michavila .

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