Worm Travails

A rubber string is 10 meters long. A worm crawls from one end to the other at 1 meter/hr. After each hour the string stretches to become 1 meter longer than it's last length.Will it reach the end ?

Yes, the worm will reach the end because at the end of every hour when rubber band stretches, the distance travelled by the worm in past hr(s) will also increase and remaining distance to travel becomes less as compared to earlier.

For exapmle:
at the end of 1st hour:
worm has tarvelled: 1meter

Now, when the whole length of rubber band becomes 11m then effective distance travelled by the worm in past 1hr becomes 1.1 merter.

if we calculate remaining distance to travel: 11 - 1.1 = 9.9 meters

Clearly it has reduced from 10 metres .... :-)

Clock Puzzle

There is a clock at the bottom of the hill and a clock at the top of the hill. The clock at the bottom of the hill works fine but the clock at the top doesn't. How will you synchronize the two clocks. Obviously, you can't carry either of the clocks up or down the hill! And you have a horse to help you transport yourself. And, the time required for going up the hill is not equal to the time required to go down the hill.


Answer : You have to go up the hill and come back, with horse, without horse, getting four equations to solve four unknowns - time to go uphill - with horse, without horse, time to go downhill - with horse, without horse. Then you can go up the hill and set the clock to '(time when you left) + (time to go uphill with horse)'