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On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

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How good are you at estimating angles?

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LOGO Challenge 8 - Rhombi

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

Half Past Two

Stage: 3 Short Challenge Level: Challenge Level:1

clock at 2.30
In moving from one number on the clock face to the next, a hand moves $360 \div 12 ^\circ = 30 ^\circ$.
At 2.30, the hour hand will be exactly half way between the $2$ and the $3$, and the minute hand will be exactly on the $6$.
So the angle between the two hands will be $3 \times 30^\circ + 15^\circ = 105^\circ$.

This problem is taken from the UKMT Mathematical Challenges.