3

Part of 1999 Hungary-Israel Binational

Problems(2)

Hungary-Israel Binational 1999\3

Source: functional equation from Q to R

Find all functions

f:\mathbb{Q}\to\mathbb{R}

that satisfy f(x\plus{}y)\equal{}f(x)f(y)\minus{}f(xy)\plus{}1 for every

x,y\in\mathbb{Q}

functioninductionalgebra unsolvedalgebra

Hungary-Israel Binational 1999\6

Source: Maximal number of examinees

In a multiple-choice test, there are 4 problems, each having 3 possible answers. In some group of examinees, it turned out that for every 3 of them, there was a question that each of them gave a different answer to. What is the maximal number of examinees in this group?

combinatorics unsolvedcombinatorics