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1.) Circular References
A factory has a circular work cell,
which they wish to divide into four equal
sections, using three safety curtains, each
the same length. How might this be done?
Extra Credit: What is the length of the
three safety curtains?
2.) The Circling Cart
That same factory has a four wheel cart that rides on a pair of circular tracks.
The outside wheels of the cart turn twice
as fast as the inner wheels. The cart's axles
are 5 feet wide.
What is the length of the
3.) Ancient Riddle
This is a very old story - you may have
heard it. It's often told regarding 17 cows,
but we couldn't help taking a small liberty:
An eccentric automation tycoon passes
away, leaving his empire (consisting of 17
factories) to his children in the following
manner: his eldest is to receive half of his
factories, his second child - one third of
the factories, and his youngest gets one
ninth of them. The children do not wish
to share or 'break up' a factory, and thus
they cannot figure out how to divide
They consult a wise friend (also an
automation expert) who offers to loan them
a factory, so that with a total of 18 factories;
the eldest can take half (or 9 factories), the
second child gets the one third share (6
factories), the youngest child receives the
one ninth share (2 factories) AND they can
give the 'loaned' factory back to the friend.
The three children also realize that they are
each better off in the end, than they would
have been if they had subdivided one of
Can you explain the apparent paradox
in simple mathematical terms?
4.) Tooling Around
In one well-automated factory, the
operators were getting bored, so the
foreman offered them a challenge. The
factory has 25 CNC machine tools arranged
in a neat grid of 5 rows, and 5 columns.
Each machine tool has an operator. The
foreman offered to let each operator
move to a new machine tool as long as
they followed certain restrictions. Each
operator could only move to a machine
tool that was in the position directly in
front, or directly behind, or directly to
the right side, or directly to the left side -
of that operator's original position. All of
the operators were required to move, and
in the end there must be an operator at
Were the operators able to meet the
foreman's restrictions? Why or why not?
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The Break Room, Issue 25, 2013