### Brain Teasers

# 3:15pm

Once more, Mad Ade is waiting for the local Kebab shop to open.

He glances at his clock and notices the time is 3:15pm. Out of sheer boredom Mad Ade works out the angle between the minute and hour hand.

What was the angle between the hour and the minute hands at 3:15pm?

He glances at his clock and notices the time is 3:15pm. Out of sheer boredom Mad Ade works out the angle between the minute and hour hand.

What was the angle between the hour and the minute hands at 3:15pm?

### Answer

7.5 degreesAt 3:15, the minute hand will be perfectly horizontal pointing towards 3, whereas the hour hand will be moving towards 4. Also, the hour hand must have covered 1/4 of angle between 3 and 4.

The angle between two adjacent digits is 360/12 = 30 degrees.

Hence, 1/4 of it is 7.5 degrees.

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## Comments

Shouldn't this be under Math, not Logic?

it fits both.

Either 7.5 or 352.5 (I was hoping for 352.5, actually), and I fail to see the logic in this puzzle. A fun problem to solve for its simplicity.

Gosh, me being stupid, i thought there wouldn't be any angle because they would be diretly on line! Am I Stupid or What?

don't worry about it Cheesy, most people do, that was one of the main premises of the teaser.

The answer is zero degrees.

I realize I am mistaken. I have my logic. However, I fail to see how the answer works...

At 30 the hour hand would be on the 3, or at 0 degrees in a standard cartesian coordinate system. The minute hand is at 12, or 90 degrees. The hour hand moves one-twelfth of 360 degrees, or 30 degrees, every hour. Therefore, in fifteen minutes (1/4 hour) it moves 7.5 degrees. In the same time, the minute hand moves to the 3, which is 0 degrees. So the angle between the two hands is 7.5 degrees

Yippeee!

One with no kebabs and I think made-ade can actually do this one!

One with no kebabs and I think made-ade can actually do this one!

the answer isnt zero cuz as the minutes pass the hour hand will slowly move towards the other hour. it wont just make a huge jump to the other hour every 59 minutes and 59 seconds

it should be under math, and it was too easy for a 2ΒΌ difficulty rating.

I bet you acctually sat there and worked it out didn't you.These kind of teasers,are just no fun,its just like doing maths homework all over again

I agree with those who state that this should be under math. If MAD ADE still thinks logic could he please explain why logic.

The reason this is in Logic (IMHO) is that the actual math involved in this puzzle is trivial. Getting to the math and figuring out the approach, how to solve this, and why it needs solving in the first place (of the first glance the angle ia 0), now that is all logic

I agree with sakirski. The math is trivial once you get past the fact that it will not be zero degress, but the zero degrees part of it is probably the biggest hurdle. AGTMA... Another Great Teaser Mad-Ade.

mad-ade claims to have a proof showing how to trisect a 60 degree angle with a straight edge and compass

Excellent teaser! I was a bit slow on the uptake even with the answer, but my mini mental paradigm shift was fun!

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