34th Eötvös 1930 Problem 1 How many integers (1) have 5 decimal digits, (2) have last digit 6, and (3) are divisible by 3?
We can write the number as d 4 d 3 d 2 d 1 6. There are 10 choices for each of d 1 , d 2 , d 3 . Now if the digit sum of the other digits is 0, d 4 must be 3, 6 or 9. If it is 1, d 4 must be 2, 5 or 8. If it is 2, d 4 must be 1, 4, or 7. So in any case we have three choices for d 4 . Hence 3000 possibilities in all. 34th Eötvös 1930 © John Scholes jscholes@kalva.demon.co.uk 1 Nov 2003 Last corrected/updated 1 Nov 03