- #1

thetexan

- 257

- 11

This has bothered me for quite some time. This drawing represents the plastic ring around your typical 6-pack of Dr. Peppers, Coke or most any 6 pack of something. The ring consists of 6 loops for the drinks, two small internal loops, and one handle loop. As any good dolphin lover would do I take a pair of scissors and make cuts through the plastic to "un-loop" all of the loops. It always takes a minimum of nine cuts...double cuts through more than one side is not allowed. Nine cuts!

I swear I did it in 8 cuts one time, and I was and have always been careful in my count, because I want to know. I have never been able to recreate the sequence of cuts that resulted in just 8 cuts. It always takes 9 no matter how I go about it. My question is this...is there a mathematical topographical way to prove the minimum number of cuts necessary to eliminate all of the loops? If so what's the answer. Is it 9 or can it be done in 8? Here is an even better question...if 8 is possible, why is the sequence of those 8 cuts so elusive? What makes that sequence so special that it's so hard to find, assuming its exists as I am convinced it does?

So until proven otherwise I am going to call this the Texan Conjecture which states..."Given the above diagram, there is a number of cuts less than nine that will result in a complete unlooping of the given loops".

Now, I go to start my Wikipedia page....

Tex

Tex

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