# Understand the problem

Each lottery ticket has a 9-digit number, which uses only the digits 1, 2, 3. Each ticket is coloured red, blue or green. If two tickets have numbers which differ in all nine places, then the tickets have different colours. Ticket 122222222 is red, and ticket 222222222 is green. What colour is ticket 123123123?

##### Source of the problem

Indian National Olympiad 2003

##### Topic

Combinatorics

##### Difficulty Level

Medium

##### Suggested Book

An Excursion in Mathematics

##### Challenge

Show that the colour depends only on the first digit.

# Start with hints

Do you really need a hint? Try it first!

Note that 311311311 is blue.

Note that, 211311311 is either green or blue. Comparing with 333133133 and previous data, show that it cannot be blue.

Hint 2 implies that 211311311 is green. Comparing 123123123 with tickets obtained, we conclude that it has to be red.

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# Connected Program at Cheenta

#### Math Olympiad Program

Math Olympiad is the greatest and most challenging academic contest for school students. Brilliant school students from over 100 countries participate in it every year. Cheenta works with small groups of gifted students through an intense training program. It is a deeply personalized journey toward intellectual prowess and technical sophistication.