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by Gavin Kistner

The NPR show "Car Talk" has regular quizzes that they call "Puzzlers"[1]. The
one listed on their web site for March 12th[2] is titled "Getting to 100". In
the quiz, you are supposed to write down the digits 1-9 in order, followed by "
= 100", and then insert between them two minus symbols and one plus symbol (in
any order) to make the formula correct. You aren't allowed to re-arrange digits,
or do some toothpick math like combine two minus signs to make a plus. You must
use every digit, and all three operators. For example, here's one incorrect
solution:

	123 + 45 - 67 - 89 = 100  (This is an incorrect formula; it totals 12)

The quiz, then, is to solve this problem without thinking, instead letting the
computer think for you. Your program should output every possible equation that
can be formed, and the actual result of that equation. The equation that results
in 100 should have stars around it. At the end, you should print out the number
of formulae that were possible. Here's an excerpt of some example output:

	...
	12 - 34 - 567 + 89 = -500
	12 - 34 + 567 - 89 = 456
	12 + 34 - 567 - 89 = -610
	************************
	123 - 45 - 67 + 89 = 100
	************************
	123456 - 7 - 8 + 9 = 123450
	123456 - 7 + 8 - 9 = 123448
	123456 + 7 - 8 - 9 = 123446
	...
	168 possible equations tested

You should not print the same equation more than once. ("1 - 2 - 3 + 456789" is
the same as "1 - 2 - 3 + 456789", even if the computer thinks that the two minus
symbols come in a different order.)

Extra Credit: Write your program to accept an arbitrary number and ordering of
digits, an arbitrary set of operators (but allowing the same operator more than
once), and an arbitrary target number that the equation is supposed to evaluate
to.

	[1] 2007 Puzzler Index: http://www.cartalk.com/content/puzzler/2007.html
	[2] http://www.cartalk.com/content/puzzler/transcripts/200711/index.html