HMMT 十一月 2008 · 冲刺赛 · 第 28 题
HMMT November 2008 — Guts Round — Problem 28
题目详情
- [ 14 ] Johnny the grad student is typing all the integers from 1 to ∞ , in order. The 2 on his computer is broken however, so he just skips any number with a 2. What’s the 2008th number he types?
解析
- [ 14 ] Johnny the grad student is typing all the integers from 1 to ∞ , in order. The 2 on his computer is broken however, so he just skips any number with a 2. What’s the 2008th number he types? Answer: 3781 Write 2008 in base 9 as 2671, and interpret the result as a base 10 number such that the base 9 digits 2 , 3 , . . . 8 correspond to the base 10 digits 3 , 4 , . . . 9. This gives an answer of 3781.