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MathNet 2022-part-02 — 197 problems (EN–VI) Question 103

Math Olympiad Vault · MathNet 2022-part-02 — 197 problems (EN–VI)

Question 103

The government of Bosnia and Herzegovina has decided to introduce a new system of licence plates. Each licence plate must contain 8 digits, each of which can be $0,1,2,3,4,5,6,7,8$ or $9$. Moreover, two distinct licence plates must always have at least two different digits. For example, if it puts the plate $00000000$ into circulation, the government will not be able to put the plate $00010000$ into circulation.

Find the maximum number of licence plates the government can put into circulation.