Valery Ochkov (Russian text, Another articles)

The part of the Book «Mathcad 8 Pro for Students and Engineers»

CompuretPress Public House, 1999

Solving some problem we sometimes have difficulties. The problem can have two
alternate solutions, and all «for» equal all
«against». What do we have to do in this case? Do you
have to go to business trip? Do you buy one more hard disk for computer? Our
life sets us difficult problems!

Someone
throws a coin, other thinks
about man or woman and looks through the window and waits, who first will
appear. But all these are not scientific methods. The coin can roll somewhere,
and there is no one in he street except a cat for hours...

But
there is method of decision-making that is verified by centuries. It is enough
to play patience. If it coincide, the solution is made, otherwise it is not. We
can find other reasons for its advantage and make a reality of it.

To
make a decision such way sometimes very difficult, there is not always a pack
of cards, and you can not play patience during working day. But you can do it
on the screen of the display. In Windows, for example, there are
plays-patiences; but we think out something new, but the main thing it will be
more entertaining and
instructive. We play the ancient patience “Turkish Handkerchief” in Mathcad.
There are three reasons for it:

1.To know better the program, we have to try to
solve some problem. The problem must be very unsuitable. One can say it is distortion, but see etude 3 of the Book.

2.In childhood every normal man broke toys for
looking how they work. And we look how the park of cards is shuffled and played
patience too.

3.By tradition to guess on
cards and to play patience, it is allowed only at Christmastide[1]. Our patience is
numeric puzzle and we can play it the year round.

Mathcad-document
(see GIF-Picture and Mathcad
WorkSheet) allows to play the patience «Turkish handkerchief» by next
rules. From one shuffled pack of cards (52 cards) is put five lines by 10 cards
in every line. Last two cards are put in six inexact line, in any place, for
example, in first or second columns. We have to straighten the «handkerchief», putting off from
different columns for one step two lower cards – kings, queens, aces and etc.

For
putting cards off, it is necessary to copy right part of the operator P = ... (it is the matrix) on free place,
and to make the cursor to
necessary text constant (to a card) and to click left button of the mouse and
to press the button Delete. There is an empty square instead of a
number.

From
played patience we put off two twain.
Then we can put off two eight, two kings or two ten (question- what do we put
off from three pairs). After it new cards will open. If we can open all 52
cards, it means that I have to go to business trip and I have to buy a hard
disk.

Compiling the program formed the matrix P (play patience) is useful for learning the base notions, for example,
vector, matrix, of linear algebra. When we compiling the matrix P, the matrix Suit
transposes (matrix with one line transforms to matrix with one column, that is
a vector). Then with help of the function stack new non-shuffled pack of cards is formed, where one sorted out suit
follows the other (vector Pack). In cycle with parameter (for...)
with help of the cycle while[2] and the function rnd*, *shuffled
pack of cards is formed, that is the vector Shuffled_Pack, that double cycle
with two parameters (for... for...) in
the end of the program is put by layers to the matrix Patience.

The
program formed the matrix P, we can develop, make this program to reject not solved layout, for example, in one column
there are three or four identical cards. There is more difficult not
solved layout, two pairs of cards criss-cross cover each other. It will be
useful for working in Mathcad with matrix operators and functions. But there is
more difficult task for readers: to form the program that itself played
patience or at the worst it informed that the patience could be solved by
putting off any pair of open cards. More clever policy is choice of a card from three or four
identical open cards.

Besides
linear algebra our program affects other interesting parts of mathematics:* *probability theory,* *statistician (see function rnd, that generate pseudorandom numbers).
Next question is interesting too: can we form a program calculating probability
of convergence of some patience? It is considered that the patience
«Solitaire», including to the standard Windows, is solved all time and it does
not depend on initial layouts…

Very
often one can do everything perfect when one do it playing and with great
pleasure, for example, walks, speaks, swims and etc. Author, for example,
learned to count before school with help of pack of cards. Queen is three, king
is four and so on. Now author tells to his students, that the main thing you
get from study is pleasure and only after it knowledge. Man spends his life all
for nothing if he does not get pleasure from his work, study. For example, if
you cannot understand linear algebra, then you have to relax and try to get
pleasure.

To begin to study vectors and matrices (data file) in course of information science
one can meet with built-in functions and operators of a program. But one can
play patience.