Using your Head is Permitted

March 2015 riddle

Last month, Qiyang Lu challenged us with the following riddle:

Let ABCD be a quadrilateral with side lengths abcd and diagonal lengths e and f. Prove or disprove: e+fa+b+c.

Several readers sent in their ideas for related inequalities. In particular, Radu-Alexandru Todor sent in a whole bunch of such inequalities and related problems. Here are three of his inequalities, which you can try to prove (or disprove!) this month.

  1. e+fa+b+d.
  2. e+f ≤ 0.5a+1.5b+0.5c+0.5d.
  3. e+fa+b+(√2-1)c+(√2-1)d.

I will stress that Radu not only wrote this month's riddle for me, but also wrote up the entire solution which I will present at the end of the month. Thanks Radu!

In a break from tradition, I will not be soliciting reader proofs this month. and there will be no list of solvers. Please only send in a solution if you think that it is so extraordinarily elegant that I may want to integrate it alongside Radu's original solution.

No List of solvers this month.

Elegant and original solutions can be submitted to the puzzlemaster at Names of solvers will be posted on this page. Notify if you don't want your name to be mentioned.

The solution will be published at the end of the month.


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