HMMT 二月 2001 · 冲刺赛 · 第 1 题

HMMT February 2001 — Guts Round — Problem 1

[5] January 3, 1911 was an odd date as its abbreviated representation, 1/3/1911, can be written using only odd digits (note all four digits are written for the year). To the nearest month, how many months will have elapsed between the most recent odd date and the next odd date (today is 3/3/2001, an even date).

解析

[5] January 3, 1911 was an odd date as its abbreviated representation, 1/3/1911, can be written using only odd digits (note all four digits are written for the year). To the nearest month, how many months will have elapsed between the most recent odd date and the next odd date (today is 3/3/2001, an even date). Solution: The most recent odd date was 11/19/1999 (November has 30 days, but the assumption that it has 31 days does not change the answer), and the next odd date will be 1/1/3111. From 11/19/1999 to 1/1/2000 is about 1 month. From 2000 to 3111 is 1111 years, or 12 · 1111 = 13332 months, so the total number of months is 13333 .