2

Part of 2002 Bundeswettbewerb Mathematik

Problems(2)

Source:

Each lottery ticket has a 9-digit numbers, which uses only the digits 1, 2, 3. Each ticket is colored red, blue or green. If two tickets have numbers which differ in all nine places, then the tickets have different colors. Ticket 122222222 is red, and ticket 222222222 is green. What color is ticket 123123123? (a) Green (b) Red (c) Blue (d) Data insufficient

sequence & representation

Source: germany 2002

We consider the sequences strictely increasing

(a_0,a_1,...)

of naturals which have the following property : For every natural

n

, there is exactly one representation of

n

a_i+2a_j+4a_k

i,j,k

can be equal. Prove that there is exactly a such sequence and find

a_{2002}

algebra unsolvedalgebra