Who Wants to be a Millionaire?

Discrete Mathematics Level 4

When you enter the "Who Wants to be a Millionaire? " competition, you are asked to write down a six-digit number $$\overline { abcdef }$$. The winning number is also a six-digit number that looks like $$\overline { uvwxyz }$$. If your six-digit number has at least 1 pair of consecutive digits that is exactly the same as a pair of consecutive digits from the winning number, then you are a winner! What is the least amount tickets you have to buy to ensure that you will win at least once?

*Note: $$\overline { ab }$$=$$\overline { uv }$$, $$\overline { bc }$$=$$\overline { vw }$$... and $$\overline { ef }$$=$$\overline { yz }$$ are valid

However, something like $$\overline { ab }$$=$$\overline {wx }$$ or $$\overline { ab }$$=$$\overline { yz }$$ are invalid

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