2

Part of 2006 Hungary-Israel Binational

Problems(2)

Hungary-Israel Binational 2006_2

Source:

A block of size

a\times b\times c

1\times 1\times 2

domino blocks. Assuming that each of the three possible directions of domino blocks occurs equally many times, what are the possible values of

a

b

c

combinatorics unsolvedcombinatorics

Hungary-Israel Binational 2006_5

Source:

x

y

z

are nonnegative real numbers with the sum

1

, find the maximum value of S \equal{} x^2(y \plus{} z) \plus{} y^2(z \plus{} x) \plus{} z^2(x \plus{} y) and C \equal{} x^2y \plus{} y^2z \plus{} z^2x.

symmetryinequalities unsolvedinequalities