8

Part of 2011 JBMO Shortlist

Problems(2)

decipher (LARN-ACA): (CYP +RUS) = CYP RUS,

Source: JBMO 2011 Shortlist A8

Decipher the equality

(\overline{LARN} -\overline{ACA}) : (\overline{CYP} +\overline{RUS}) = C^{Y^P} \cdot R^{U^S}

where different symbols correspond to different digits and equal symbols correspond to equal digits. It is also supposed that all these digits are different from

0

reflection of vertices wrt diagonal not outside polygon

Source: JBMO 2011 Shortlist C8

Determine the polygons with

n

(n \ge 4)

, not necessarily convex, which satisfy the property that the reflection of every vertex of polygon with respect to every diagonal of the polygon does not fall outside the polygon. Note: Each segment joining two non-neighboring vertices of the polygon is a diagonal. The reflection is considered with respect to the support line of the diagonal.

reflectionJBMOcombinatoricscombinatorial geometry