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MathNet 2006 — Part 02 Question 193

Math Olympiad Vault · MathNet 2006 — Part 02

Question 193

Telephone exchange extensions have only 2 digits, from $00$ to $99$. Not all extensions are in use. Changing the order of two digits of an extension in use, you either get the same number or a number of an extension that is not in use. The largest possible number of extensions in use are:

(A) Less than $45$

(B) $45$

(C) between $45$ and $55$

(D) more than $55$

(E) $55$