October 31, 2001: Boo! Wish
I had a ghostly program to post today, but I've been kind of occupied with
maintenance stuff. The shared border problem is
fixed -- the index on each program page is again complete. The Google search button has also returned to the bottom
of the index column on Program pages.
October
28, 2001: At last the Roller
Coaster Simulation program has been posted. Back in
mid-September when I posted the Simple Rolling Cart predecessor, I thought
that a couple of weeks would be plenty to finish the coaster.
Wrong! But it does work pretty well and allows users to design and
save tracks with hills and loops and even warns when your riders may
not survive the ride.
October 20, 2001: What is the
lowest number that can be divided by 6 with a remainder of 5; by 5
with remainder 4; and by 4 with remainder 3? (Mensa
Puzzle Calendar, October 18, 2001). Or the original Chinese
version:
We have a
number of things, but we do not know exactly how many. If we count them
by
threes we have two left over. If we count them by fives we have three
left over. If we count
them by sevens we have two left over. How many things are there?."
The Chinese scholar, Sun Zi, provided
a rather obscure poem about septuagenarians and plum trees as a solution (at best a hint, it seems to me).
With or without poems as hints, Chinese Remainder problems seem quite difficult
to solve without a computer. With Delphi we can solve them with this
Beginner's level Chinese
Remainder program of about 50 lines of code. A second
longer version is included which does better error checking and allows
larger problems to be solved
We are still fighting problems with
left shared borders in
the Programs section. The Programs section home page has a complete
index of program entries. The index on other program pages is missing
at least the current Chinese Remainders entry.
October 15, 2001: A recent Business Week article
discussed the current youth fad of clothing with numbers.
That gave me the idea for a line of T-shirts with "interesting"
numbers on the front and the reason that they are interesting printed on
the back. Here's a sample shirt back: "The 3 digit
number with the most divisors". What number appears
on the front? Most Divisors
is a beginners level program that provides the answer.
October 9, 2001: Page formats should be OK
again. Some of you may have thought it was just lousy design
that eliminated the index to other pages within the Programs,
Delphi-Techniques and Math-Topics sections of our site. It was good
design , just lousy implementation of a bright idea I had last week - but
I now understand "Shared borders" and "Navigation
bars". (I
hope).
Here's a program that solves the "9321
problem". Insert operators between the digits to form
expressions that evaluate to 0,1,2,...,9. Operators are +, -,
*, and /. So, for example, 9-3*2+1=4. Our
program generates valid solutions by trying all 64 permutations of
operators.
October 1, 2001: Many of you puzzlers will
recall that it takes 23 randomly chosen people to have a better than
50-50 chance that at least two share the same birthday. But
what if those odds aren't good enough? How large a group will we
need to be 90% sure that duplicate birthdays occur? The
solution requires only about 5 lines of Delphi code. (well OK, 50 lines,
but Delphi generates the most of them.)
To get the code (and the answer to the question),
check this
Shared Birthdays Math Topics page.
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