Maths Nerds......

[Bobrob]

I'm agreed on that 1 so how's about a new riddle
On an ordinary clock face using just the hours and minutes hands how many right angles are made in 24 hours

 

[Reptile Smile]

Hmmph. Maybe missing something on this one. Surely, for any position of the hour hand, there exist two positions that the minute hand could be in that are at right angles. So isn't the answer two times infinity..?

Or 'infinity', if you prefer...

 

[Gaz #68]

2 right angles every minute. 60 minutes per hour and 24 hours. 2x60x24 = 2880. Could be wrong though

 

[Reptile Smile]

But the hour hand occupies positions in between the 'minute' positions..? I think it's more...

Though - I do think your solution is more where the question intends.

 

[Gaz #68]

The hour hand moves between the minute positions but the minute hand will only be at 90 degrees to it twice per cycle. As the hour hand moves between the individual minute positions the minute hand will be sweeping around so only makes the two right angles once per sweep. At other times in its sweep it wont be at 90 degrees but the hour hand will still be moving between the minute marks. That's the logic I have gone for.

 

[Cook$]

More threads like this.

 

[Reptile Smile]

The hour hand moves between the minute positions but the minute hand will only be at 90 degrees to it twice per cycle. As the hour hand moves between the individual minute positions the minute hand will be sweeping around so only makes the two right angles once per sweep. At other times in its sweep it wont be at 90 degrees but the hour hand will still be moving between the minute marks. That's the logic I have gone for.

Yup, am with you, but for me the flaw is that the hour hand isn't discrete - it doesn't move in one 'chunk' from minute 47 (say) to minute 48. It moves continuously, like the minute hand, so because the hour hand can occupy any point, there are (at any point) two positions the minute hand can be that are at right angles to it. But if you're right - if the minute hand does move discretely from position to position, then I agree with you.

How about: by what factor is the number of rectangles on a chessboard larger than the number of squares?

 

[Liam92]

its all based on the fact that the hour hand spins at a ratio of 1:12 the speed of the minute hand, so its not like the minute hand actually hits 90 degrees twice every hour.
in 24 hours the hour hand will spin twice, and the minute hand will spin a total of 24. so as it spins round it overtakes the hour hand 22 times. every time it passes it has to make 90 degrees twice in a 360 degree spin so it should be 44 right angles in total. it makes your head go fuzzy picturing it but i figured it out by sitting staring at a picture of a clock for about 10 minutes while a customer was on hold and i was pretending to be investigating a billing issue...

 

[Reptile Smile]

God, I was talking absolute ****e, wasn't I? I'd totally lost track of the thing about it being it within 24 hours.

Had to go get a clock and try it. Liam's nailed it - good job, sir! Definitely 44...

 

[Liam92]

Yup, am with you, but for me the flaw is that the hour hand isn't discrete - it doesn't move in one 'chunk' from minute 47 (say) to minute 48. It moves continuously, like the minute hand, so because the hour hand can occupy any point, there are (at any point) two positions the minute hand can be that are at right angles to it. But if you're right - if the minute hand does move discretely from position to position, then I agree with you.

How about: by what factor is the number of rectangles on a chessboard larger than the number of squares?

I'm gonna go for 5.25 as many rectangles as squares

edit: i'll wait for another couple answers before i give away my working haha