PUMaC 2014 · 团队赛 · 第 1 题
PUMaC 2014 — Team Round — Problem 1
题目详情
- [ 4 ] The evilest number 666 has 1881 digits. Let a be the sum of digits of 666 666 and let b be the sum of digits of a and let c be the sum of digits of b . Find c . o
解析
- [ 4 ] The evilest number 666 has 1881 digits. Let a be the sum of digits of 666 and let b be the sum of digits of a and let c be the sum of digits of b . Find c Solutions We see that a < 1881 × 9 has atmost 5 digits. Hence b < 5 × 9 has at most 2 digits. Since 666 9 | 666 , we see that 9 | a and hence 9 | b . Thus b ∈ { 9 , 18 , 27 , 36 } and c = 9 . o