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Imagine you are in a rectangular room 3meters wide, 5 meters long and 3 meters high. At 2 opposing ends of the room therefore is a square wall 3 meters wide and 3 meters high. On the vertical centre line one of these square walls is a black dot 1 meter from the floor. On the vertical centre line of the opposing square wall is a black dot 1 meter from the ceiling i.e. 2 meters from the floor.
You have a marker pen and your task is to draw a single continuous line connecting both the dots. You can draw on any of the walls plus the floor and the ceiling if you wish. Assume all walls are perfectly vertical, and the floor and ceiling perfectly horizontal
What is the shortest line you can draw to join the 2 dots?
You have a marker pen and your task is to draw a single continuous line connecting both the dots. You can draw on any of the walls plus the floor and the ceiling if you wish. Assume all walls are perfectly vertical, and the floor and ceiling perfectly horizontal
What is the shortest line you can draw to join the 2 dots?
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It doesn't matter where the room is. It may have windows but thats nothing to do with the question or the solution.
sorry (13^2 + 1^2) ^(1/2)= 13 and a bit. that is further than the line down the centre of the room. How can 13 not be right?
13 is the answer, and it's the answer whether you draw along the walls OR the ceiling OR the floor.
Ipso facto imo.
Ipso facto imo.
13 is not the answer. a priori: from the former. If you think something a priori, you are conceiving it before seeing the facts.
13 isn't the answer i don't think.
i think it would be shorter if you went sideways from the dot, and then at a slight angle along the wall (rather than along the floor or ceiling).
i think it would be shorter if you went sideways from the dot, and then at a slight angle along the wall (rather than along the floor or ceiling).
no, if you went at a slight angle the answer would be 170^1/2 which is a bit further than 13m.
Kev
The room is 5 metres long.
7M is wrong I have just realised.
The room is 5 metres long.
7M is wrong I have just realised.
Sorry Kev,I didn't realise you'd increased the size of your room after asking the original question based on the room being 5 metres long.Sorry.
No worries Gene. It was my mistake. It can be done in less than 13 meters though.
my room disagrees. Please just put me out of my misery. How can it be done?
I just can't see how you can beat a straight line.
I just can't see how you can beat a straight line.
evski. If you have drawn the room, you can't be too far away from the solution.
It couldn't be anywhere near as short as 10.05 metres, the room is 10 metres long.
The door is not important for the solution.
The door is not important for the solution.
Impossible to answer without knowing more about the door.
Kev, I think you are wrong. 13m is the shortest line. I have drawn a 2x scale room on graph paper and it tells me the answer is 13
i'll have to give up then. i can't get it less than 13.
i can't think of anything else though kev. i've been trying for an hour!
ffs kev, just tell us your fecking answer, or is this a wind-up?
munch man and evski. Do you know pythagoras theorem?
lol no evski, I swear i've done this fing puzzle before
yes, i do kev, that was what my answers were based on
I think the door opens inwards and is the height of the point on the one side.
yes. a^2+b^2=c^2
If you are using pythagoras the shortest a is 13 and the shortest b is 1 leading to 170^1/2 which is more than 13
If you are using pythagoras the shortest a is 13 and the shortest b is 1 leading to 170^1/2 which is more than 13
Agreed, get sqrt 170 also, think you need to form another triangle of some sort
well being over 1hr since original post doesn't make it a 'quick' christmas question. I hate false advertising.
evski. You can make a right handed triangle from the dots 12.5 long & 3.5 high.
if we use a side wall the minimum length is 13 because 2x1.5 +10 =13 even if the dots are the same height.
if we use the ceiling or the roof the sum to the floor/celiing at each end is min of 3m which again makes a min of 13
if we use the ceiling or the roof the sum to the floor/celiing at each end is min of 3m which again makes a min of 13
but the line would have to be in thin air then kev, no?
can you tell us kev please, i have to go out in a bit.
Have we confirmed that the door opens inwards? And is the door painted?
Give me 5 minutes. I am just working on an explanation. It isn't easy without drawing it.
he's told us the answer - its root 168.5. the question is how do you get that
does the line go along the side AND bottom walls?
this is wrong. If you make a plan and flatten it there is a straight line between the two dots, any deviation from this line increases the length.
Sorry kev but you have phooked it up. The only way to explain the alternative would be to use the angles, which I suspect are imprecise.
Sorry kev but you have phooked it up. The only way to explain the alternative would be to use the angles, which I suspect are imprecise.
imagine yr looking at the room from the side. if u imagine one end is turned out to face u and the other end is dropped down flat u then draw a line between the points that goes along the bottom AND side of the room
Ok, imagine the room opened up as a flat piece of paper.
The floor is 3M wide & 10M High. Above and below is an adjacent square 3M x 3M.
The lower dot is on the centre line of the floor plan 1 metre beyond the end of the floor plan. Draw a line 3.5M to the right then 12.5M up. The end of the 12.5M line is at the point where the dot would be on the opposite wall. The line which connects those 2 points is the hypotenuse of a 3.5M high, 12.5M wide right angled triangle. Its length is 12.98M.
I hope thats clear enough?
The floor is 3M wide & 10M High. Above and below is an adjacent square 3M x 3M.
The lower dot is on the centre line of the floor plan 1 metre beyond the end of the floor plan. Draw a line 3.5M to the right then 12.5M up. The end of the 12.5M line is at the point where the dot would be on the opposite wall. The line which connects those 2 points is the hypotenuse of a 3.5M high, 12.5M wide right angled triangle. Its length is 12.98M.
I hope thats clear enough?
13 is the shortest. if you start using triangles and hypoteneuses then the answer is actually longer whichever way you do it
p.s. a cardboard box for a hair clipper helps!
nah, the answer is 13, I'm sorry but neither of those answers approaches clarity. It is an impossibility to go below 13 metres.
proof:
Call the wall with the dot 2m from the floor A and the other B. As the ceiling and floor are identical in proportions to the walls we will cal them walls for simplicity.
The closest A is to a wall is 1m. The minimum distance to the other wall is 10m. Once we get to A the shortest distance to the dot is 2m. QED.
proof:
Call the wall with the dot 2m from the floor A and the other B. As the ceiling and floor are identical in proportions to the walls we will cal them walls for simplicity.
The closest A is to a wall is 1m. The minimum distance to the other wall is 10m. Once we get to A the shortest distance to the dot is 2m. QED.
u have to imagine that imagine each wall of the room opened out and laid out flat - if u did this u would easily see what the shortest line is (it goes along the bottom (or top) and also the side walls). the easiest way to understand is to get a cardboard box
A cardboard box 10 meters long is not easy to come by !
I still think the location and size of the door is the key here.
if you lay out the box it makes a rectangle with the dimensions 16x3. The two dots lie on the center line and the distance between them is 13m. It is a straight line and cannot therefore be longer than any other route, the answer is 13m. Unless someone can provide a mathematical proof I'm not happy with the "I've drawn it answer"
kev you've a git, I've wasted about an hour doing this ;)
kev you've a git, I've wasted about an hour doing this ;)
there is no door - u are trapped forever and the walls are starting to close in....
if you lay out the box it makes a rectangle with the dimensions 16x3
??????
??????
Easy when you think about it tbh ;) As long as it isnt another couple of years before I come across this puzzle again i'll know the answer
Sorry evski you have just not seen it yet. If you were stood in the room looking at the actual dot 1 metre up from the floor, the line would go from that dot almost vetically down to the floor but just left of vertical, it would then head in a straight line until it met the long wall to your left about halfway along its base, if you then turned around it would head for a point about halfway up the right hand side of the 3M square wall behind you then straight for the dot 1 metre from the ceiling.
of course u need the ability to think in at least 7 dimensions to understand the explanation
Cheers Don. They say a pictures worth a thousand words.
Right, I've sussed it. **g hell, that nesse my brain up.
best not get started on the 12 ball problem!! :^0
interestingly the right answer is less than 2cm shorter than the obvious 'straight line' answer of 13m, so its hardly worth the bother!!
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