How many integers (1) have 5 decimal digits, (2) have last digit 6, and (3) are divisible by 3?
Solution
We can write the number as d4d3d2d16. There are 10 choices for each of d1, d2, d3. Now if the digit sum of the other digits is 0, d4 must be 3, 6 or 9. If it is 1, d4 must be 2, 5 or 8. If it is 2, d4 must be 1, 4, or 7. So in any case we have three choices for d4. Hence 3000 possibilities in all.
© John Scholes
jscholes@kalva.demon.co.uk
1 Nov 2003
Last corrected/updated 1 Nov 03