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MathNet 2020 — Math Olympiad Vault — Part 05 Question 64

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 05

Question 64

We call a telephone number $d_{1} d_{2} d_{3}-d_{4} d_{5} d_{6} d_{7}$ nice if the number $d_{1} d_{2} d_{3}$ equals $d_{4} d_{5} d_{6}$ or $d_{5} d_{6} d_{7}$. For example, $234-2347$ is a nice telephone number. Assume each $d_i$ can be any digit from 0 to 9. How many nice telephone numbers are there?