AMC 10 Step by Step
2001 AMC 10Problem 13P11-15~4 minPrint

A telephone number has the form ABC-DEF-GHIJ\text{ABC-DEF-GHIJ} , where each letter represents a different digit. The digits in each part of the number are in decreasing order; that is, A>B>CA > B > C , D>E>FD > E > F , and G>H>I>JG > H > I > J . Furthermore, DD , EE , and FF are consecutive even digits; GG , HH , II , and JJ are consecutive odd digits; and A+B+C=9A + B + C = 9 . Find AA .

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site. Also appeared as 2001 12 #6.