On 12/7/06, Fred lunnon <fred.lunnon@gmail.com> wrote:
Huh --- scooped! I haven't chased up the article, but if they look that similar, the chances are they're the same problem.
OK, try this one for size instead (quite literally) --- Four cities, lying on a circle, are linked by straight roads, each stretching an integer number of miles. If the circle has radius 147, what lengths do the roads have?
A square root sign had gone AWOL in the above, as they have a habit of doing every so often. That should have read --- Four cities, lying on a circle, are linked by straight roads, each stretching an integer number of miles. If the circle has radius 50, what possible lengths might the roads have? Apologies to everybody. WFL
On 12/3/06, Joshua Zucker <joshua.zucker@gmail.com> wrote:
On 12/2/06, Fred lunnon <fred.lunnon@gmail.com> wrote:
Since I can't meet Ed's challenge, I'll substitute a (gentler) problem of my own ----
Four cities, no three lying on a straight line, are linked by straight roads, each stretching an integer number of miles. The first road is 2 miles long; how long are the other five?
I think this problem, or maybe just a similar one, is solved in Ian Stewart's column entitled "A six-pack for the tree gods", collected in his book _Another Vine Math You've Got Me Into_ if memory serves me, which it may not ...
--Joshua Zucker
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