Subj:.....Primitive
Railroading Problem (S620)
From the book
"Mathematical Puzzles of Sam Loyd"
Edited by Martin Gardner
From: Dover Publications in 1959
Find
the simplest method by which the trains
can
pass.
In this specimen of
primitive railroading we have an
engine and four cars
meeting an engine with three cars.
The problem is to
ascertain the most expeditious way of
passing the two trains
by means of the side-track, which
is only large enough
to hold one engine or one car at a
time.
No ropes, poles or
flying switches are to be used, and
it is understood
that a car cannot be connected to the
front of an engine.
How many times is it necessary to
back or reverse the
directions of the engines to
accomplish the feat,
each reversal of an engine being
counted as a move
in the solution?
. .
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THE SOLUTION
1. Back the
R engine far out to the right.
2. Run the
R engine on to the switch.
3. Run L engine
with three cars goes out to the right of the switch.
4. R engine
backs to the main track.
5. R engine
with three cars, goes to the left of the switch.
6. L engine
on to the switch.
7. R engine
and three cars connects with the four cars
to the right of the switch.
8. R engine
pulls all seven cars to the left of the switch.
9. L engine
returns to the main track.
10. L engine backs
to the train.
11. L engine pulls
five cars to the right of the switch.
12. L engine backs
the rear car on to the switch.
13. L engine draws
four cars to the right.
14. L engine backs
four cars to the train on the left.
15. L engine goes
alone to the right of the switch.
16. L engine backs
up to the switch.
17. L engine pulls
the car from the switch to the main track.
18. L engine with
one car backs up to the train on the left.
19. L engine goes
forward to the right with six cars.
20. L engine backs
rear car on to the switch.
21. L engine goes
right with five cars.
22. L engine backs
five cars to the train on the left.
23. L engine goes
right with one car.
24. L engine backs
up to the switch.
25. L engine goes
right with two cars.
26. L engine backs
to the train to the left of the switch.
27. L engine draws
all seven cars to the right of the switch.
28. L engine backs
the end car on to the switch.
29. L engine goes
right with six cars.
30. R engine backs
to the train on the right.
31. R engine picks
up its four cars and leaves to the left.
32. L engine backs to
the switch.
33. L train picks
up its third car and leaves to the right.
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