数学之家

标题: 2010年Puzzleup数学竞赛−第20题:Digital Watch [打印本页]

作者: zyzme    时间: 2010-12-19 18:12
标题: 2010年Puzzleup数学竞赛−第20题:Digital Watch
                                     Digital Watch

You have a digital watch showing the hour, the minute and the second in 24-hour notation. (example: 00:12:59, 23:45:00 etc.)
At some time you look at your watch and observe that these six digits are all different.
If you replace all the digits with the number of pieces used to show the corresponding numeral in the digital layout,
then you get a new time, which also has the property of consisting of six different digits.

At what time, the difference between those two times are maximum?

Example: If the time was 01:23:45, then we get 62:55:45 from the number of pieces on the digital layout. But it is not a valid time in 24-hour notation.

The number of pieces for all digits in digital layout are as follows: (six for 0, two for 1, five for 2, five for 3, four for 4, five for 5, six for 6, three for 7, seven for 8, six for 9)

Enter your answer as six digits, without using spaces or colons. That is to say, enter 012345 for 01:23:45.





欢迎光临 数学之家 (http://www.2math.cn/) Powered by Discuz! X3.1