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Speedy Sidney

Two trains set off at the same time from each end of a single straight railway line. A very fast bee starts off in front of the first train and flies continuously back and forth between the two trains. How far does Sidney fly before he is squashed between the two trains?

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Rule of Three

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

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Digital Times

Which segment on a digital clock is lit most each day? Which segment is lit least? Does it make any difference if it is set to 12 hours or 24 hours?

Walking in the Mountains

Stage: 3 Short Challenge Level: Challenge Level:1
Before lunch Peter and Heidi have walked for $60$ minutes covering a distance which the sign indicates should take $1$ hour and $40$ minutes. So the pair take only $\frac{60}{100}=\frac{3}{5}$ of the time indicated by the sign. They stop for $15$ minutes, then cover the remaining distance in $\frac{3}{5}\times 75=45$ minutes. The journey takes $60+15+45=120$ minutes in total, so they reach Salzbau at $2$pm.

This problem is taken from the UKMT Mathematical Challenges.