19th Eötvös 1912 Problem 1 How many n-digit decimal integers have all digits 1, 2 or 3. How many also contain each of 1, 2, 3 at least once?
3 choices for each digit, so 3 n in all. We must exclude the 2 n with all digits 1 or 2, and the 2 n with all digits 2 or 3, and the 2 n with all digits 1 or 3. But then we exclude twice those with all digits 1, all digits 2 and all digits 3. Hence 3 n - 3·2 n + 3. 19th Eötvös 1912 © John Scholes jscholes@kalva.demon.co.uk 29 Oct 2003 Last corrected/updated 29 Oct 03