### Need of Speed For Average Speed

A man drives

**1 mile**to the top of a hill at**15 mph**. How fast must he drive**1 mile**down the other side to average**30 mph**for the 2-mile trip?**Here is calculation of that speed needed!**Something to tease your brain!

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A man drives 1 mile to the top of a hill at 15 mph. That means he took, 1/15 hours i.e

To achieve average speed of

Let

30 = 2/(1/15 + 1/x)

(1/15 + 1/x) = 2 / 30 = 1/15

1/x = 0

To conclude, it's impossible to achieve average speed of 30mph in trip.

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Four glasses are placed on the **corners** of a** square** table. Some of the
glasses are **upright **(up) and some **upside-down** (down). A blindfolded
person is seated next to the table and is required to re-arrange the
glasses so that they are **all up **or** all down**, either arrangement being
acceptable, which will be signaled by the **ringing **of a bell.

The glasses may be re-arranged in turns subject to the following rules.

1.Any**
two glasses** may be inspected in** one turn** and after feeling their
orientation the person may reverse the orientation of either, neither or
both glasses.

2.After each turn the table is rotated through a**random**
angle.

3.The puzzle is to devise an algorithm which allows the blindfolded person to ensure that all glasses have the same orientation (either up or down) in a finite number of turns. The algorithm must be non-stochastic i.e. it must not depend on** luck.**

**Here is that algorithm!**

The glasses may be re-arranged in turns subject to the following rules.

1.Any

2.After each turn the table is rotated through a

3.The puzzle is to devise an algorithm which allows the blindfolded person to ensure that all glasses have the same orientation (either up or down) in a finite number of turns. The algorithm must be non-stochastic i.e. it must not depend on

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At this point, the position of other 2 glasses is not known.

If the bell does not ring then there are now three glasses up and one down(

And if you find both are up, then you must have chosen other

If so, then turn one down so that

And in case, if you find one is up and other down like -

still

Now

The