Creative Problem Solving

**Kilgamayan** · 09-1-2006, 03:18 PM

I'm taking this course right now and it seems like the kind of thing a lot of people here would enjoy. It's basically a course full of "make four liters using only a three-liter jug and a five-liter jug"-type problems, although those problems are, of course, the easiest to solve.

Try some:

- Let a, b and c be positive numbers. Prove that (a/b) + (b/c) + (c/a) >= 3.
- For which real numbers c is there a straight line that intersects the curve y = (x^4) + 9(x^3) + c(x^2) + 9x + 4 at four distinct points?
- How many arithmetic problems of the following form are possible? You must use each of the digits 1 through 9 in numerical order from left to right, and you can use any combination of the + and * symbols as you like provided your syntax is still correct. Proper examples include 123+45*6789, 1+2+3+4+5*6+7+89 and 123456789, while 12+3*+456++78*9 does not count.

Now obviously I'm not going to ask any questions where I don't already know the answer, so don't bother accusing me of not doing my own homework. >_>

09-1-2006, 03:18 PM	#1
Kilgamayan Super Scooter Happy Join Date: Feb 2003 Location: Location, Location. Age: 41 Posts: 6,583	Creative Problem Solving I'm taking this course right now and it seems like the kind of thing a lot of people here would enjoy. It's basically a course full of "make four liters using only a three-liter jug and a five-liter jug"-type problems, although those problems are, of course, the easiest to solve. Try some: - Let a, b and c be positive numbers. Prove that (a/b) + (b/c) + (c/a) >= 3. - For which real numbers c is there a straight line that intersects the curve y = (x^4) + 9(x^3) + c(x^2) + 9x + 4 at four distinct points? - How many arithmetic problems of the following form are possible? You must use each of the digits 1 through 9 in numerical order from left to right, and you can use any combination of the + and * symbols as you like provided your syntax is still correct. Proper examples include 123+456789, 1+2+3+4+56+7+89 and 123456789, while 12+3+456++789 does not count. Now obviously I'm not going to ask any questions where I don't already know the answer, so don't bother accusing me of not doing my own homework. >_> __________________ I watched clouds awobbly from the floor o' that kayak. Souls cross ages like clouds cross skies, an' tho' a cloud's shape nor hue nor size don't stay the same, it's still a cloud an' so is a soul. Who can say where the cloud's blowed from or who the soul'll be 'morrow? Only Sonmi the east an' the west an' the compass an' the atlas, yay, only the atlas o' clouds.

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