Being a teacher, I am constantly coming up with math problems for my students to solve that say the least. I find that these type of problems are a motivation for our more advanced students to think outside the box and to really take the process of thinking mathematically to the extreme.

So, being the math nerdfighters, I was wondering if I could poll your brains for problems you have pondered (either of your own creation or from other sources). I personally would love to try to think my way through a few.

As an example, here's one I pondered for a while:

Oddie is tied to pole in John's backyard by a 15 foot rope. Oddie, as always, gets picked on my Garfield who prompts him to run around the pole in circles. The rope wraps around the pole at a rate of 4 inches per rotation (so the effective radius of the circle decreases by 4 inches every time Oddie completes a 360° arc). The question is: How far (as in distance, not number of times around the pole) does Oddie run before the rope is completely wrapped around the pole?

I look forward to seeing your mind twisters and any solutions you may have to mine little puzzle.


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This website is a GOLD MINE of challenging, mind-boggling math problems.


As for your problem (very nice, btw) I think I figured it out.
I made an assumption here, and that was for every revolution around the pole, the distance is the average of the circumference at the beginning of the revolution and the end of the revolution. So for the first revolution, it would be the average of 30 pi and 29 1/3 pi which would be 29 2/3 pi. Every average circumference for each successive revolution decreases by 2/3 pi; the last revolution has an average circumference of 1/3 foot; there are 45 revolutions. Using arithmetic sequences, we know that n=45, a(sub 1)=1/3 pi, and a(sub n)=29 1/3 pi. Using the formula for the sum of an arithmetic sequence, S(sub n)= n[a(sub 1)+a(sub n)]/2, the answer is 45x(30 pi)/2 which would equal 675 pi feet.

Gah, math problems like this are my weakness. Whenever I see something like this, I can't just not try and figure it out. o_o
I'm glad I gave you something entertaining :) I came up with this problem while giving my Algebra 2 students some work on Conic Sections. I will wait a few more day (probably until after Monday) before I post the solution I came up with.

I like your thought process, which of course is what I'm actually looking for. I've learned that there is an infinite number of ways to arrive at an answer, so I hope I see many different methods of reaching a solution to the problem.
What was the actual answer to this problem? It's been quite a while since my attempt to solve it.

Is it ( this is an estimate) 45 times around the circle? My worst and oddest problem: a per son drops one thousand pLund of feathers out of
a plain flying over the ocean at 20000 feet and ten seconds later drops a thousand pound of led out. Which hit the ground first?
The lead will actually hit the ground that is at the bottom of the ocean, while the feathers will just float on top.

That's more of a physics problem than math...
Am I the only one who get's a nerdgasm looking at this problem??? I should certianly hope not. This looks like fun. I look foward to solving it. I guess what excites me so much about something like this is that its like a solving a puzzle. Unfortunatly I think it's missing a few pieces or there are too many variables to get an exact answer. How thick is the rope? As it wraps around does it pile on top of itself effectively increasing the radius of the pole or does it wind upward on the pole making the remaining length of the rope the hypotenuse of a triangle with the distance Oddie is from the pole as one leg, and the appropriate portion of the pole as the other. Also, how tall is the pole? Where on the pole is the rope tied? How tall is Oddie? I suppose we could also equate the elasticity of the rope, how hard Oddie is pulling, and whether or not Oddie is following a spiral with the rope pulled tight or if he simply walks back and forth on either side of the pole on each pass, but that may be going a bit too far.
I suppose the simplest answer would be to assume that the pole is the only protrusion on the surface area of the circle and that the rope isn't tied at a secure spot alowing to simply pivot on the spot. In this case Oddie would continue to walk in an uninterpted circle into infinity or until the ding of the oven causing John's latest lasagna recepe to lure Garfield away from his helpless attepmts to torment Oddie into a dizzy noose. Then again, the radius decrease described in problem seems to debunk ths option.

On an unrlated note, here's a problem I've come accross that I found interesting at the very least. It's more like false evidence. Even the best of mathematicians can easily over look the basic rule that makes this evidence false. See if you can find it.

Asume x=1
Therefore x-x=0
Also 2x-2x=0
Therfore x-x=2x-2x
Destributive property tells us that 1(x-x)=2(x-x)
Now if we divide both sides by (x-x)
what do we get? 1=2???

Nerds.0625^(-1/2) ever!!! DFTBA
you can't divide by zero, and x-x = 0
One of my favourites from a Further Maths lesson last year. I don't remember what we were meant to be doing, but we ended up working out how many oranges could fit in the classroom, taking into account squishyness and the fact that oranges don't tessellate, so don't fill all the space. That was a good one. Yesterday, we worked out how fast you would go on a rope swing across the Grand Canyon if there was no air resistance. Turns out, if the rope is somehow anchored to be perfectly horizontal initially, it goes at over 1000 metres a second.
I know the Ohio State University Ross Mathematics Program usually has some good application problems you can try.


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