A discrete mathematics problem by Shenal Kotuwewatta

Discrete Mathematics Level 3

Peter created a cool problem to post on Brilliant, but he don't have a cool name for that.

So he decided wrote a simple program which outputs a string of 7 letters.

(The letters are from A-Z, and the same letter may be repeated.)

Call a name pronounceable if vowels and consonants appear alternatively in that name. The probability that the name of Peter's problem is pronounceable is \(\frac{p}{q}\) where \(p\) and \(q\) are coprime positive integers. What is the last \(3\) digits of \(p+q\)?


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