Fly to the cube of sugar?

[Josie]

jane has placed a sugar cube at a point on the wall of a living room one foot from the floor and six feet from each corner. A fly with a broken wing is standing on the opposite side wall one foot from the ceiling and six feet from each corner. If the living room is thirty feet long, twelve feet high, and twelve feet wide, what is the shortest path along which the fly should walk to get from where it is to the cube of sugar?

[WaldoMcFroog]

Okay, well, the fly absolutely has to walk the thirty feet of the length of the room. That is not negotiable. The trick is in how it gets to the length of the room - by wall or by ceiling.

The fly therefore has two routes:

Route1: Walk directly sideways along the wall to the corner (six feet), maintaining its one foot above the floor at all times. Turn and walk along the length of the wall (30 feet) until it reaches the next corner and walk to the sugar lump (six feet). Thus, the fly has walked 6+30+6 = 42 feet.

Route2: Walk directly up the wall to the ceiling (11 feet (the wall is 12 feet, and the fly is already one foot off the floor)). Turn and walk along the length of the ceiling (30 feet) until it reaches the next corner and walk down to the sugar lump (11 feet). Thus, the fly has walked 11+30+11 = 52 feet.

Therefore, it is quicker to walk along the wall.

Now all we have to do is establish whether Jane broke the fly's wing in order to test a mathematical problem (in which case, she's a sadist) or whether she's trying to encourage the fly to get better by feeding it (in which case, she's an oddball).

[WaldoMcFroog]

Of course, an even shorter route would be to walk down the wall (1 foot), across the room (30 ft), up the other side (1 foot), making a total of 32 feet. The only problem is that Jane's such a loony, she's probably built punji pits or something.

[SKCOLL]

In the second answer walking down the wall would cost you 11 ft + 30 ft + 1 Ft = 42ft. Walking along the middle of the floor or the middle of the ceiling gives you the same answer. Route 3 - Taking the shortest diagonal path along the walls sqrt(42*42 + 10*10) gives you 43.17m. Can the fly drop without having to walk? - can he autogyrate like a helicopter and get to the floor? therefore walking only the length of the floor and 1 ft up? = 31ft?

[pinus]

I make it 40.00 feet Root (32^2 + 24^2) The route goes diagonally across end wall, ceiling, side wall, other end wall I'm off to catch the last post, and will do another check on my Pythagoras when I get back.

[pinus]

My sketch is not to scale, so the route probably includes the floor as well.

[tomd]

40.0, if you draw a net of the room with the fly & sugar lump both you can make a triangle 24m x 32m that it can walk the hypotenuse of. I'd show you my drawing but i haven't got a scanner.

[SKCOLL]

With a nice round number 40 sounds good but I can't visualise the path. I don't see why the fly should go up to the ceiling - surely that increases the distance. Fly 11m from floor, sugar 1m from floor - so you want to keep the 10m distance on the Height Axix minimised? Or am I lost again?

[tomd]

I don't know why it's shorter, but if you draw it out on paper it works. Doesn't make much sense, he would cut across the corner of the ceiling, down a side wall, slightly across the floor then up the opposite wall.

[tomd]

He goes down the 1ft and cuts off the corner of the room rather than walking right to the edge, I see it now.

[bernardo]

A similar question was asked a while ago in which the room was 40ft by 10ft and the fly and sugar cube were a spider and a fly. But the mathematical idea is the same.

diagram

Actually I drew the two path lines in purple and green but the scanner didn't seem to notice.

[SKCOLL]

I once was lost - now I'm found. Nice one chaps & chappesses

[WaldoMcFroog]

Pants. I wish I hadn't misread the question - I thought the fly was in the same relative position as the sugar. I am a twit!

[penshk]

the fly walks down the one foot of the wall he's own, acroos the thirty foot livig room and up the one foot on the other side. I get 32 feet. Not sure but draw it out.

[penshk]

Sorry that would be up the wall to where the fly sits 42 feet. 11+30+1. In reverse it would be the same. Oh well I tried to help!