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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?

Question Setters

Stage: 3 Short Challenge Level: Challenge Level:1

Rudolf takes one hour to set $30$ questions, so he takes $2$ minutes to set each question. We're told each person takes half as long as the previous person to set questions, so we can work out how long each person takes to set one question, then multiply by the number of questions to give the time each setter spent on all their questions:

Time taken to set each question (minutes)
Number of questions set Total time spent setting questions (minutes)
John $8$ $25$ $200$
Peter $4$ $26$ $104$
Rudolf $2$ $30$ $60$
Susie $1$ $39$ $39$
Tony $\frac{1}{2}$ $55$ $27 \frac{1}{2}$

So in total the setters spent: $$ 200+104+69+39+27 \frac{1}{2} \;\text{minutes}= 430 \frac{1}{2} \text{minutes} $$ or $$7 \; \text{hours } \; 10 \; \text{minutes }\; 30 \; \text{seconds }$$ setting questions.

This problem is taken from the UKMT Mathematical Challenges.