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Angle Time (Angle Anguish in the UK version) is a puzzle in Professor Layton and the Last Specter.

Puzzle

US Version

Have you noticed that throughout the 24 hours of the day there are special times, like 1:11, at which the same digit appears three times in a row?

If you take these special times and measure the angle clockwise from the hour hand to minute hand, excluding angles where 12 lies between the two hands, which time has the greatest angle?

Obviously, the angle between the hands in times like 00:01 and 00:09 is tiny, so you can ignore those form the start.

UK Version

Have you ever noticed that throughout the 24 hours of the day there are special times, like 01:11, at which the same digit appears three times in a row?

If you take these special times and measure the angle going clockwise from the hour hand to minute hand, excluding times where 12 lies between the hands, for which time is the angle greatest?

Firstly, the angle between the hands in times between 00:00 and 00:09 is tiny, so you can ignore those.

Hints




Click a Tab to reveal the Hint.

US Version

First, try to think of all the times in a day that have the same number three times in a row. There might be too many to remember, so use the Memo function.

Also, why would the puzzle note times like 00:01 or 00:09?

UK Version

First, try to think of all the times in a day that have the same number three times in a row. There might be too many to remember, so use the Memo Function.

Ignore any angles that you would measure going from the minute hand to the hour hand.

Additionally, the largest angle is greater than 180 degrees, so you can disregard any angle you find that's less than that.

US Version

Are you sure you didn't miss some times? When you express the times in 24-hour format, you'll have more possibilities to consider than with a 12-hour format.

In addition to 11:11 and 22:22, there are 31 possible choices. If you didn't find that many already, you may have overlooked something. Try to relax and think about the problem again.

UK Version

Are you sure you didn't miss some times? When you express the times in 24-hour format, you'll have more possibilities to consider than with a 12-hour format. 00:00 to 00:09 have already been excluded. In addition to 11:11 and 22:22, there are now 31 times with three of the same digit in a row.

If you didn't find that many, you may have overlooked something. Try to relax and think about the problem again.

US Version

The following times that have three identical numbers in a row have an hour-hand-to-minute-hand angle of more than 180 degrees: 14:44, 15:55, 22:23 to 22:29, and 23:33.

Which of these times can be excluded because 12 lies inside the angle you measure? If you just think a little longer, you should get it.

UK Version

There are several times that have both three identical numbers in a row and an angle of more than 180 degrees between the hour and minute hand: 14:44, 15:55, 22:23 to 22:29, and 23:33. Now, which of these times can be excluded because 12 lies inside the angle you measure? Just think a bit longer and you should get it.


Solution

Incorrect

US Version

Too bad!

Perhaps you overlooked something. Try reading the question again.

UK Version

Bad luck!

Perhaps you overlooked something. Try reading the question again.

Correct

Correct!

US Version

The answer is 15:55. On an analog clock, 3:55 and 15:55 look the same, but only one has three identical digits!

The 24-hour clock didn't stump you!

UK Version

The answer is 15:55. On an analogue clock 03:55 and 15:55 look the same, but only one has three identical digits.

LS042S

A big thanks to http://professorlayton4walkthrough.blogspot.com

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