The Games and Puzzles Journal, #5+6 - Mayhematics

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TI{E GAMES AND PUZZI,ES JOURNAL
Get My Goat
The diagram shows Tom MARLow's clever
solution to the 'G et My Goat' puz z\e (p 40
of issue 3 ). The f ence is a di f f erent shape,
but still encloses the goat, thus f ulf illing
the conditions of the problem. The sequence
is: 9GI?G, 93453, T 63b4, G ZL}T, GZT g.
Mr Marlow also reported that the solution
to problem c75b) in sl,ding, pigqe puzzles
can be reduced by one E-ove: In tffi
for C75(a) change move Ig2 to gDR and 1gB
to 10LD, complete the zll moves and add gLU.
Stiding Magic Sguares
The following technical notes left over from Len Gordon's article in the last issue may
be of interest to readers who have computers with which to tackle these problems.
It is not often that a computer search can improve on long-standing solutions to
a difficult and popular puzzle. Dudeney ran a newspaper puzzle column, so the results
he presents in his books often reflect the best of his readers. The very nature of a truly
good puzzle is that it is not amenable to 'brute force' seareh. Simple tests luckily ruled
out most of the magic squares quickly, but a fair percentage had to be tested by sliding.
The search time increases exponentially with the number of solution steps.
Reported times are for a compiled BASIC program on a 2.8 Mhz TRS-80. For this
lVRe of problem on an 8-bit machine, compiled programs usually run about b0 times as
fast as ordinary BASIC' and about 1/8 as fast as assembly language programs. Since
completing this study I have switched to an 8 Mhz IBM-pc type of computer and am using
a QuickBASIC compiler. This has resulted in a speed-uf factor of abolt 4.b. In addition-,
John Harris has contributed some ideas and between us we have sped the program by
another factor of 6 or 8. However, we are still short of the speed needed to iolie worsi
cases.
An ABC Slrdrng Block Puzzle
By Jerry GORDON
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This puz zl,e, invented in May this year, may
interest your readers. It has 8 square pieces
on a 3 x 3 base. Three pairs of the bi.ces
combine to show the letters A, B, c. The
case illustrated is one of zg positions solved
and has a unique solution in f ewest moves"
Letter Zig-Zags
By Vladimir PRIBYLINEC
Here are three puzzles with letters. The pieces carrying the letters move along the
rows' columns and diagonals to the last free square in the ciosen course. you musf find
the shortest way to spell out the determined word on any row of the diagram in fewest moves.
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