Page 28

THE
   MEN TAL
          MAZE
   By CLIFTON FONSTAD, JR. ee4
APHIL means that you have
     only this one more chance
     to win a Maze Master award
this year. Next month's answers
will be given after the problems
and there will be no May Maze
Master. So that you can get to the
puzzles quickly then, we'll cut the
words of wisdom short and simply
make note of the fact that the
Mental Maze is just packed with
illustrations and good puzzles to
go with them this month.
  Now, let's get started on the
first puzzle-the first turn in this
months Mental Maze.
  1. The first puzzle is one for the
industrial engineers. Anyone can
work it though so have a go at it.
  If a tinker and his helper can
refabulate a widgit in 2 days, and
if the tinker working with his
apprentice instead would take 3
days, while the helper and the
apprentice would take 6 days to
do the job, how long would it
take each working alone to re-
fahulate the widgit?
  2. Here's an interesting problem
sent down from a fan at Tioga
Tech. One of the landmarks on
the Tech campus is a large tower
with a clock at the top. This clock
tolls out the hours as regularly
today as it did fifty years ago but
it has changed some. When the
clock was installed it took it eight
seconds to strike eight; now it
takes six seconds to strike six.
  Our question is-how many sec-
onds does it take the clock to strike
twelve? How long did it take
originally?
  3. If you're still with us and
didn't get tricked too badly by the
last couple turns in the maze see
if you can get past this next one.
28
  Suppose you want to construct
the following figure out of match-
sticks. In the center is a square
with an integral number of match-
sticks on each side. Then using
each side of the square as a base
four triangles are constructed-
each is different and each has
sides made with an integral num-
ber of matchsticks. The result
looks like the diagram below
where a, b, c, are integers repre-
senting the number of matcbsticks
in each line.
  What is the minimum number
of matchsticks that can be used
to form such a figure?
b
S
C-
-f
h
4. The last puzzle might have
taken a while so let's try a couple
shorter ones.
  In a domino set that runs up to
double-six, there are 28 pieces or
bones. In a set that runs up to
double-nine there are 55 bones.
How many bones are there in a
domino set that runs up to double-
twelve? Who would want a
domino set that big?
  5. Now, for those of you with
money here is a coin shuffing prob-
lem. Start out with four pennies
and four nickels placed alternately
in a row as shown below.
  * @   0   @    0    00
  *       e      o  o   o   o 0
    One move is made by moving
  any two adjacent coins together
  to another position on the line.
  Make four such moves and rear-
  range the coins in a line so that
  all the pennies and all the nickels
  are together as shown in the sec-
  ond drawing.
    6. To close out April's maze try
  playing with a little Algebra.
  There are three computers in the
  basement of the Lesser Antilles
  and Farther North Studies Build-
  ing on campus. Computer A is as
  old as computers B and C to-
  gether. Last year B was twice as
  old as C and in two vears com-
  puter A will be twice as old as
  computer C. How old are the three
  computers?
  ANSWERS
    The answers to last month's
  Mental Maze are:
    1. 2/5
    2. 54,45 years
    3. 70 yards
        13485_ 13845 _ 14865
        2697    2769     2973
              18645
              - 3729
    5. 5 men
    6. 416 pages
    This is your last chance to win
  a Maze Master award and the five
  dollars that goes with it because
  next month we have to publish
  the answers with the Maze. So
  hurry and send your solutions to
  the Mental Maze, Wisconsin Engi-
  neer, 333 Mechanical Engineering,
  University of Wisconsin, Madison.
  Remember, too, you don't have to
  have all the correct answers to
  win.
THE WISCONSIN ENGINEER