What is the smallest number with exactly 14 divisors?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?
Observing that triangle $PQS$ is isosceles, we have $\angle PSQ = \frac {1}{2}(180^{\circ} - 12^{\circ}) = 84^{\circ}$ and hence $\angle PSR = 180^{\circ} - 84^{\circ}=96^{\circ}$. Since triagle $PRS$ is also isosceles, we have $\angle SPR = \frac {1}{2}(180^{\circ} - 96^{\circ}) = 42^{\circ}$. Hence $\angle QPR = 12^{\circ}+ 42^{\circ} = 54^{\circ}$.
This problem is taken from the UKMT Mathematical Challenges.