360 AnswersEH and CF dotted lines instead of CD and GH. Having fixed our four
shortest lines, the remainder may all be drawn in one continuous line from
A to K, as shown. When you get to D you must run up to C and back to D,
from G go to H and back, and so on. Or you can wait until you get to C and
go to D and back, etc. The dotted lines will thus be gone over twice and the
method shown gives us the minimum distance that must be thus repeated.
- WATER, GAS, AND ELECTRICITY
This puzzle can only be solved by a trick. If one householder will allow one
pipe for a neighbor to pass through his house there is no difficulty, and the
conditions did not prohibit this not very unreasonable arrangement. Look at
Figure I, and you will see that the water pipe for supplying house C passes
through house A, but no pipe anywhere crosses another pipe. I am, however,
often asked to prove that there is no solution without any trick, and I will now
give such a proof for the first time in a book.
Assume that only two houses, A and B, are to be supplied. The relative
positions of the various buildings clearly make no difference whatever. I give
two positions for the two houses in Figures 2 and 3. Wherever you build
those houses the effect will be the same-one of the supply stations will be
cut off. In the examples it will be seen that if you build a third house on the1