Using your Head is Permitted

December 2011 riddle

A big thank you to Claudio Baiocchi who suggested this month's riddle as another follow-up to the October riddle. Further references for this riddle will be given on the solution page.

In the country of Mathematica, post offices have parcels shaped like tetrahedra, rather than boxes. The price of sending a parcel is proportional to the sum of the six sides of the parcel.

Is it still true that it is not possible to place a higher-priced parcel inside a cheaper parcel? If not, what is the highest-priced parcel that can fit into a parcel that costs x to send?

Prove your answer.

NB - This month solvers are encouraged, but not mandated, to provide a solution for simplexes in any dimension.

List of solvers:

Radu-Alexandru Todor (14 December 09:40)
Dan Dima (21 December 00:41)

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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