[Guest]

When a ten year old boy Tim wanted to know the current time, his uncle Jonathan looked at his 12 hour analog wristwatch, and replied, “At the next four minutes, it will be exactly ten times as many seconds after the half -hour as it was minutes before the same half- hour last time the two hands were in right angles this afternoon.”

Determine the current time, assuming that the above conversation took place after 12:00 p.m. but before 12:00 a.m.

Edited April 1, 2009 by K Sengupta

[Guest]

After 12 pm. It says right in the riddle this afternoon.

[Guest]

After 12 pm. It says right in the riddle this afternoon.

Nice attempt, but the term "after 12:00 p.m. but before 12:00 a.m" was appended only for the sake of clarity.

The puzzle is easier than it looks. We have to look for a time in the afternoon (that is after 12:00 p.m.) that satisfies all the given conditions.

Edited April 1, 2009 by K Sengupta

[Guest]

3:31?

[Guest]

A fifteen year old boy was apprehended in his appartment earlier today. Circumstances around the crime scene suggests the boy was responsible for the murder of his own uncle. The boy was living with his uncle at the time. Speculations about motives point towards years of psycological torture towards the boy and that his uncle actively ensured he was never on time for anything.

Off topic, of course, but if that was my uncle and I was ten, I probably would have punched him... hard.

[HoustonHokie]

When a ten year old boy Tim wanted to know the current time, his uncle Jonathan looked at his 12 hour analog wristwatch, and replied, "At the next four minutes, it will be exactly ten times as many seconds after the half -hour as it was minutes before the same half- hour last time the two hands were in right angles this afternoon."

Determine the current time, assuming that the above conversation took place after 12:00 p.m. but before 12:00 a.m.

Three questions:

1. Does the phrase "at the next four minutes" indicate that the uncle is referring to the next even increment of 4 minutes (i.e., 12:04, 12:08, 12:12, etc.) or does it mean four minutes from the current time?

2. Do you mean whole minutes/seconds, or do you consider the decimal portion of those numbers as well?

3. Are the two hands in referred to the hour and minute, or the minute and second?

[Guest]

6:28 and 30s?

[Guest]

actually 3:31 makes more sense being exact right angles..

[Guest]

Three questions:

1. Does the phrase "at the next four minutes" indicate that the uncle is referring to the next even increment of 4 minutes (i.e., 12:04, 12:08, 12:12, etc.) or does it mean four minutes from the current time?

2. Do you mean whole minutes/seconds, or do you consider the decimal portion of those numbers as well?

3. Are the two hands in referred to the hour and minute, or the minute and second?

Clarification:

“The time when the two hands were in right angles, the hour hand and the minute hand were precisely situated on two distinct minute marks.”

I now understand that this portion should have been included in conformity with the intent of the problem.

1. The phrase "at the next four minutes" means four minutes from the current time.

2. Already follows from the clarification.

3. The two hands correspond to the hour hand and the minute hand.

[bonanova]

Either 3:00 or 9:00.

At no other times are the hands at right angles and aligned with minute marks.

[HoustonHokie]

Either 3:00 or 9:00.

At no other times are the hands at right angles and aligned with minute marks.

So 3:31 is definitely an answer. In 4 minutes, it will be 3:35, and it will be (35-30)*60 = 300 seconds after the half hour (3:30), which is 10 times the 30 minutes it was before 3:30 at the last time the hour and minute hands were 90 degrees apart (3:00). But couldn't 9:31 also be an answer? Or does the phrase "this afternoon" disqualify so late a time?