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August 1961 Popular Science
 [Table of Contents]
Wax nostalgic about and learn from the history of early
electronics. See articles from
Popular
Science, published 1872-2021. All copyrights hereby acknowledged.
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These challenges appeared
in a 1961 issue of Popular Science magazine. They are more reminiscent of
what would be found in
The Old
Farmer's Almanac; however, that dose not mean they are easy. A variety
of geometric, mathematic, and logic puzzles are included. Some, you might have
seen proposed in a different format, like the Chief Koko dilemma of transporting
objects across a weight-limited bridge. The division problem is of the ilk still
found in some Sunday newspaper editions (the few which are still in print). The
Long Gun shipping problem requires thinking "inside the box." Consider that a
hint. The Puzzle of the Month is a variation on an old magic trick. I remember
my father having a bunch of those wire loop things.
Popular Science Puzzlers
 By Joan Steen
Tough nuts for summer cracking.
Crosses and Double-Crosses
Get out pencil, paper, scissors, pliers: I have proclaimed August Do-It-Yourself
Puzzle Month. We will begin with H. E. Dudeney's summary of Greek Cross Puzzles.
A Greek cross is made of five identical squares (right).
 Problem 1: Cut the cross into five
pieces which can be put together to form a square.
Problem 2: Improve on that: Cut the cross into four pieces all
the same size and shape and form a square. (There's only one way to do it.)
Problem 3: Try again with four cuts, this time using only two
snips of the scissors. (The pieces won't be symmetrical.) Hint: You might begin
by seeing what the length of the side of the square must be if its area is the same
as the cross.
 Now help Koko, the native chief, with his
transport problem: How can he get three choice coconuts, weighing two pounds each,
across a foot-bridge with a capacity of 250 pounds if he himself tips the scales
at 248 pounds? He can't leave any behind because the monkeys will eat them.
 Have you ever tried to crack a code? This
little division problem is as good a start as any. Like an expert decoder, you must
bring to bear on the problem whatever facts you know about the language (in this
case the number system) plus some trial and error. It's a challenging exercise .
What? another cross? A reader asks that you try drawing an X on a piece of paper
without lifting your pencil or re-crossing a line.
Which in turn reminds me of a more strenuous version: Can you tie a knot in a
piece of string without letting go of either of the ends? (Try that at a party.)
 This fellow needs your help: He's going
on vacation and he wants to take his hunting rifle with him on the train. The conductor
says, "No, sir, not on this coach!" The baggage-car attendant says, "Sorry - we're
under strict orders not to accept anything over a yard long in any dimension. Your
gun measures 1.7 yards."
Got any ideas how he can do it? Of course, ground rules prohibit any disassembling
of the gun.
 Puzzle of the Month
I warned you this was Do-It-Yourself Month. You have to construct August's :
P-O-T-M as well as solve it. (Blame Jack Gampinsky of Brooklyn, N. Y., for this.)
You need three paper clips, a pair of pliers, and a steady hand. After that you
need patience.
Clip 1 is straightened out and closed by loops at each end. (More artful souls
should attempt an arrow head at one end for reasons that will appear obvious.)
Clip 2 gets bent in a U shape and is then looped onto the arrow bar. The loops
should be slightly smaller than the end loops of the bar so that it can't slip off.
Clip 3 is more of a challenge. It's a heart that is to hang from the bar in between
the loops of the swing - imprisoned there. I caution you to follow as accurately
as you can the shape outlined here, and to be sure to slip it around the bar before
you close off the ends. For clarity we've shown the heart looped around the bottom
of the U shape. It slips around easily.
Now that you've joined these three pieces inextricably and eternally, can you
remove the heart from the end of the arrow bar without forcing any parts?
(See answers below)
Answers to PS Puzzlers
 Greek Cross. Problem 1 is fairly
easy:
Problem 2: Observe that the total area of the cross, if each side is x, is 5x2.
This means that the side of the square to be formed must be exactly x√5. Now
the cross is loaded with lines that are exactly x√5 units long - so that's your
clue. The stipulation that you find four congruent pieces (same size and shape)
suggests sliding a length of x√5 and one perpendicular to it so that the intersection
is exactly in the center of the cross. The result shows a swastika pattern.
Problem 3: Slide the perpendiculars to a point at the edge of the figure.
Koko: He juggles them. That way two are always in the air.
 Cross: Fold down a corner of the paper:
Knot in string: Cross your arms first, then pick up the ends of the string and
pull them through. As your arms unknot, the string knots.
Division Code. The product of b times b ends in b. Therefore
b is 1, 5, or 6. It's not 1 because the multiplication yields a three-digit figure.
Looking at the next step we see e - h = e. Therefore h = 0, and f times b is a number
ending in 0. If b = 5, f can be 2, 4, 6 or 8. If b = 6, f would be 5. Now observe
that at the second subtraction g - c = c. Therefore g = 2c. This implies that f
is a number bigger than b. So b can't be 6. So b = 5 and f is either 6 or 8. The
rest is trial and error: You look for the number (25, 35, 45, etc.) that, when multiplied
by 6 or 8, yields a number whose first digit is twice the second. 35 times 6 is
the only one. (The result is 210.) Therefore the original problem must have been
35√19,775 = 565.
 Long Gun. Pack the gun along the main diagonal of a box exactly
a yard by a yard by a yard. The base diagonal is √2 yards long. (By the Pythagorean
Theorem, AB2 = 12 + 12 = 2 so AB = √2.) That
side along with one of the vertical edges form the legs of another right triangle
whose hypotenuse is the main diagonal of the box. Thus we have BC2 =
12 + √22 = 3. So BC = 1.732.
Answer to Puzzle of the Month
Answer to last month's P-O-T-M: To free the heart from the wire, first slip the
heart around so that it hangs from the bottom of the swing.
Step 1: Hold the bar at the left end (if right-handed) and pick up the heart
by its point. Slip the "tongue" through the right-hand loop of the swing.
Step 2: Pull the heart and swing over to the right end of the bar and, turning
the heart so that it's horizontal, slip the tongue around the loop at the end of
the bar.
Step 3: Push the heart up and back through the loop at the same time you let
the loop drop down. Slight variants of this technique will also work. To replace
the heart, just reverse the steps.
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