South African Mathematics Olympiad

Question

The digits from 1 to 9 are added, in order, over and over again until the total is 460. 1+2+3+4+5+6+7+8+9+1+2+3+ The last digit that was added is (A) 2 (B) 4 (C) 6 (D) 8 (E) 9

Accepted Answer

The digits 1 to 9 total 45, and 460 = 10 45 + 10. So the complete set 19 will appear ten times, and then as many more digits as total 10, viz. 1+2+3+4. So the last digit is 4.