UPDATE (5 May): To clarify the bonus question: we are looking for
two polyhedra with vertices in Z^{3} that have the same number of
vertices, the same number of Z^{3} edge points, the same number of
Z^{3} surface points, the same number of Z^{3} interior points,
but two distinct volumes.The following is a classic problem. Please submit elegant solutions only, and only if you have no prior familiarity with this type of question.
Let A be their respective areas,
let _{Q}I and _{P}I be the number of
Z_{Q}^{2} points in their respective interiors, and
let B and _{P}B be the number of
Z_{Q}^{2} points on their respective boundaries (their vertices, and any
point on their edges).
The question: do there exist two such polygons with
I and
_{Q}B=_{P}B that do not have the same area?
_{Q}Either provide an example or prove nonexistence.
For a bonus mention (an asterisk next to your name), answer the same question
for two polyhedra in Z |
## List of solvers:Djinn Lu (*) (2 May 15:44)Oded Margalit (*) (4 May 00:25) Itsik Horovitz (*) (13 May 03:19) |

Elegant and original solutions can be submitted to the puzzlemaster at __riddlesbrand.scso.com__.
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.

Enjoy!