Brain teaser

[Theo O.]

At 3:17, what is the difference in degrees between the hour hand and minute hand?

[George Schilling]

At 3:17, what is the difference in degrees between the hour hand and minute hand?

The two answers that popped into my head were........

I don't know, I own digital clock

.......and zero, or close to it :king:

[Jeff Stuart]

3.5

[Will Kalman]

I got 3.5, too. Although I bet there is an interpretation of "difference in degrees" that changes the question from the obvious.

[Theo O.]

interesting so far ...

What's the one easy mistake to avoid in solving this problem?

[Michael Smith]

At 3:17, what is the difference in degrees between the hour hand and minute hand?

• temp: same temperature.
• angle: looking from the side, there is no difference.

[Theo O.]

At 3:17, what is the difference in degrees between the hour hand and minute hand?

• temp: same temperature.
• angle: looking from the side, there is no difference.

Hours and minutes, so we are talking angles and there is a difference. Now answer the question before I come down to your office

[Michael Smith]

Hours and minutes, so we are talking angles and there is a difference. Now answer the question before I come down to your office

Equation for the degrees on the hour hand
(0.5 degrees per minute on the hour hand) * (the time on the hour hand * 60 minutes per hour) + (0.5 degrees per minute on the minute hand) * (the time on the minute hand)

Equation for the degrees on the minute hand
(6 degrees per minute on the minute hand) * (the time on the minute hand)

[Jeff Stuart]

3.5 assumes it's a standard 12 hour analog clock with hands that rotate continually and at a constant rate, and that the second hand is at 12. I supposed the easy mistake to make is to calculate the answer with the hour hand pointed at the 3, rather than 17/60ths of the way to 4.

[Christine Grice]

Unless there is some major trick question twist to this one, I agree with Jeff and Will.

(17mins/60mins)*360 degrees = 102 degrees (position of min hand)
((17mins/60mins)+3hours)/12 hours)*360 degrees = 98.5 degrees (position of Hour hand)
102 -98.5 = 3.5 degrees

are we still missing something?

[Rick Brown]

Obviously could be 356.5°, too.

[Theo O.]

3.5 assumes it's a standard 12 hour analog clock with hands that rotate continually and at a constant rate, and that the second hand is at 12. I supposed the easy mistake to make is to calculate the answer with the hour hand pointed at the 3, rather than 17/60ths of the way to 4.

That's what can be missed

[Theo O.]

Unless there is some major trick question twist to this one, I agree with Jeff and Will.

(17mins/60mins)*360 degrees = 102 degrees (position of min hand)
((17mins/60mins)+3hours)/12 hours)*360 degrees = 98.5 degrees (position of Hour hand)
102 -98.5 = 3.5 degrees

are we still missing something?

Nope. You explained it perfectly

[Will Kalman]

OK, a related question.... how much time passes between each crossing of the hour and minute hand? No tricks - standard 12-hour clock, etc. Explain how you got your answer.

[Jeff Stuart]

The two hands will cross 11 times over the course of 12 hours, so

((12 hours)*(60 minutes/hour)/11 = 65.4545... minutes = 1 hour, 5 minutes, 27.27272727... seconds.

[Theo O.]

The two hands will cross 11 times over the course of 12 hours, so

(12 hours)/(11 times) = 65.4545... minutes = 1 hour, 5 minutes, 27.27272727... seconds.

Are you some sort of genius?

Nicely done.

[Jeff Stuart]

Are you some sort of genius?

Nicely done.

Heh, I like word problems, and doing these is more entertaining than work right now, unfortunately.

[Steve Ekstrand]

I got 3.5 and I went to a Liberal Arts school.

[Don Salyers]

I got 3.5 and I went to a Liberal Arts school.

But, I bet you got 3.5 right after Will did the work----

Don

[Steve Ekstrand]

Nope, I didn't scroll. Liberal Arts taught me the value of living on a path of learning and discovery. It does help that I have an old fashion school style clock staring at me on the desktop.

But after the Liberal Arts School, then I went to Business School and to Law School. Both taught me that its far simpler to just profit from the work of guys like Will.

[John Stimson]

Sunpower uses that one as a filter to automatically reject job applicants.

[Theo O.]

Sunpower uses that one as a filter to automatically reject job applicants.

That doesn't seem fair.

But then the interview for my current job was the interview from hell. 9 hours of grilling in one day by 10 people and they all have to like you. I hated all of them by the end of the day but now we are all good friends.

[Will Kalman]

The two hands will cross 11 times over the course of 12 hours, so

((12 hours)*(60 minutes/hour)/11 = 65.4545... minutes = 1 hour, 5 minutes, 27.27272727... seconds.

You got it. Many people will say "an hour", then say "oh, wait, an hour and 5 minutes", then I tell them that in that five minutes the hour hand will have moved a little more and in that time a little more and so on and on. Some people will take the bait and keep going on that path. That's where we transition from math into comedy }:)

I like to play those jokes on liberal arts grads. Later in life, you find that a little wrench twirling and they give you a co-drive seat and boot themselves out of the trophies. }:) :gpower:

[Steve Ekstrand]

[Marshall Grice]

At 3:17, what is the difference in degrees between the hour hand and minute hand?

The two answers that popped into my head were........

I don't know, I own digital clock

.......and zero, or close to it :king:

i'm with george on this one...i barely know how a dial clock works. My hour and minutes are on the same plane of lcd on my cellphone.

for the record, I failed. assumed 90deg for 3 o'clock