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Archive for January 21st, 2008

The Clock-Watcher Puzzle

The hour-hand and the minute-hand are exactly together at 12 noon.

At what time are they next together?

Intuitively, we can ‘see’ that this will happen around 1.05-1.06 pm. However, how do you solve the question mathematically?

I asked myself: On how many occasions will the two hands be together from 12 noon to 12 midnight? That is, in 12 hours how many occasions will the 2 hands be together?

A visual inspection will show 11 occasions of ‘togetherness’. So, how long does it take from one occasion of ‘togetherness’ to the next?

Since we have 11 occasions of ‘togetherness’ in 12 hours, each occasion to the next will take 12/11 hours, i.e., 1 hour and 60/11 minutes.

Working this out, the answer is 1 hour and 5.4545 minutes.

To be honest, clock-watching is not always this exciting!

Talking about clocks reminds me of that old saying.

There is no such thing as a person being ALWAYS wrong.
Why, even a clock that does not move is right twice a day!

Re-trievia recalled: Excerpts from Year 2003/ 2004
Tan Wee Kiat


Written by Ivan Chew

21 January, 2008 at 5:37 pm

Posted in Year 2003/ 2004