2001 AMC 12 Problems/Problem 6
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Problem
A telephone number has the form , where each letter represents a different digit. The digits in each part of the number are in decreasing order; that is, , , and . Furthermore, , , and are consecutive even digits; , , , and are consecutive odd digits; and . Find .
Solution
The last four digits are either or , and the other odd digit ( or ) must be , , or . Since , that digit must be . Thus the sum of the two even digits in is . must be , , or , which respectively leave the pairs and , and , or and , as the two even digits in . Only and has sum , so is , and the required first digit is 8, so the answer is .
See Also
2001 AMC 12 (Problems • Answer Key • Resources) | |
Preceded by Problem 5 |
Followed by Problem 7 |
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All AMC 12 Problems and Solutions |