TimeSpaceLightForce

@Imatfaal ..not regular queen move is required since they are not in play. Moves are more like skipping from square to square.Not touching any square below along the way. Interesting 29 visited squares (including initial position?) for a queen move! Got a path ?

Alice and the Red Queen travel across the very large Chessboard. They skim together from Square to Square without returning to the same Square. Biginning on a Square, both of them always move faster and farther than the previous trip and always land on the Square Centres..How many Squares have they visited?

@J.C.MacSwell Clear and correct..its height is not the same as its capacity. @wayne_m That's part of the atmosphere.

@Sriman Dutta When she says "it is empty" she doesnt mean "it is void" but means the glass contains no water thus full of air. Full means no air volume. Supposedly a simple logic puzzle, no physics. The truth teller would say it is not full or not empty. Also wont say it is half full or half empty. Clair would say a geater lie since she can spot the difference. Look again at that glass of water.

@sensei She can't do anything to alter the physical condition of the subject.. @JCMacSwell Assume it is as unlikely to make 1g of water appear from nothing as it is unlikely to make 1g of water disappear to nothing. @ way_m ..it is about water and glass only. Clair is not an optimist or pessimist and dont care if it is half full or half empty..She ought to choose between false and falser.

A cylindrical glass has water half its height Some say it's half full, while some say it's half empty But if Clair the liar mostly tell what's not right Will she say "it is full" or she'll say "it is empty"?

@Imatfaal Right Adjustment! Design Option Table:

@moontanman With 4x8' g.i.sheet your 4Lx2Wx2H tank should be done by cutting it into two pieces and would cost 8'cut,8'bend & 14'weld. But some 3 pieces cut,even though it cost more, gives you extra volume. -Initially she can cut 3.266 x 6.532 off any corner making the base and 2 opposite sides.

@moontanman Not enough capacity. @imatfaal Correct theoretical maximum.. but so many pieces to cut and weld not the best way for the fabricator. Maybe fewer than 5 pieces to cut will do.

The std. 4ft x 8ft ga.#16 G.I. sheet is to be fabricated (cut,bend,weld) into a large water tank. If the design is an open top box..what is the best capacity ?

Here is the mirror way done with CAD

@John Cuthber Sorry no proof..and it can not work if there's no need. If we intersect each 3 points with 3 lines forming "Y" @ 120 deg w/ each other, that will be the minimum connecting length. Unless the 3 points are making > 120 angle because the lines connecting them is already the minimum. I tried this with the cubic room where a spider web connects the 8 corners .It works With 13 segments network.All angles of the adjacent web segment are 120 degrees. e.i. for the minimum length. AutoCAD is the best for this. No math needed. Just click lines to read measurements.

@imatfaal Solved..the 120 degrees network connects n points in space with shortest line segments.

@mullimanz That is 4.91m..not bad. @John Cuthber Good sample! But not short enough.

@mordred -its ok.. -tracks means path,route,course or trail and has length .. not to be mistaken as accumulated length of foot steps. -no, going back along track will add to total length of travel..not to the track length. HINT : Imagine the pockets are towns.. what is the shortest road system to access all the towns?

@sensei The mouse makes the tracks or pathway that is as short (total length) as possible to access all 6 holes. It can go to any hole from any hole not necessarily directly or from any hole to the next adjacent hole. It can go back its track not necessarily increasing the length of track. Dont mind the distance it travels. Your proposition will be 5 meters too.. because 1-4-1-2-5-2-3-6 is the "E" route to access all pocket holes. 5 meters is wrong because it is not short enough. @ swansont The mouse can do the 1-6-middle-3-4-middle-2-5.. eventually making the crossroad where it can go back to to access the 6 holes. @ kisai 5 meters is wrong because it is not short enough. @ Mordred 5 meters is wrong because it is not short enough.

via crossroad..

1 2 3 4 5 6 connecting 1-6,3-4,2-5 is just 1+2*sqt(5)=5.472 but not short enough..

What is the least total length of the track that can be traversed by the mouse to go from hole to hole? The pool table is 2 x 1 meter.

Just omit a pipe on your layout and you got it!

@Acme : There must be a pipe to deduct on your layout that will still make it work..Almost done it! @Imatfaal : Without line #44 .. 45,40 & 50 will be cut from circuit.

@Acme Ground floor terminals are lower than the ceiling by 1 pipe length. (see diagram) Enough is not necessarily equal bulb output. Serial circuit causes 1/27 wattage output for bulbs. Additional batteries or transformer are not available. Parallel circuit is better for with a busted bulb others still lit. To try this, copy image and paste on MS Paint . there you can draw colored lines on the diagram ..

@imatfaal: Must we link to circuit or can + / - end at different nodes? Must spare 2 pipes to connect down from DC source (+) (-) on ground floor.

You can light the 27 bulbs by series connection.. that will require 29 pipes w/ single wire, but the output will not be enough. So the design is a parallel connection. Here is a connection for 5 pipes junction.

Light up the 27 bulbs on the ceilings of the building by installing 54 pipes having single wiring inside.