Obvously, I am not adept at email communications. I don’t even know what I did to get kicked out of the comment box… Moving on:
So, the next step would be to find out what the sums of the numbers in each of the sections would be. If there are 4 sections, then each section would have 78/4 as its sum. If there are 3 sections, then each section would have 78/3 as its sum.
Lucky for us, 78/4 is not an integer, which narrows the sum down to one value:78/3, or 26.
Then it is just a matter of finding how many ways there are to do this. The obvious place to start is with the 12, and see which numbers have to travel with it to equal 26
The only combination that works is 11+12+1+2=26.
That makes the rest easy. I just went to the 6, since it would have to travel in a different section than the 12 if the lines don’t intersect. Turns out that section has to have 8+7+6+5 to =26.
That leaves the middle section of 9+10+4+3=26.
VOILA! I thought it was elegant and cool, and all that other stuff. I thought sure that Ray would be explicating this or a similar approach to the solution. As he didn’t, I offer it for your perusal.
I listen to CARTALK on Sundays @ 4 pm MST,on KNAU, FLAGSTAFF, AZ, although I live just down the hill 75 miles away in Cottonwood, Az (Flagstaff is at 7000+, Cottonwood 3600 feet). Thanks. I always enjoy your show when I get a chance to hear it. Marvin