Find Total Number of Zeroes

Puzzle # 9

A certain street has 500 buildings. A sign-maker is contracted to number the houses from 1 to 500. Agreement was made such that contractor will be given with an dollar amount of total Zeroes, that he used to number the buildings?

1. Contractor follows some special Convention to earn more amount of dollars

What could be the Count of Zeroes used by contractor ?


Solution
1.Normal Way of Numbering:

        If Contractor wasn't clever then he use the normal way of numbering the building(s) i.e., 1, 2, 3, ... 500

        If he follows the above pattern so he gains and amount is :

Total Numbers between 1 and 500 that are divisible by 10     = 50

Total Numbers between 1 and 500 that are divisible by 100   = 5

Total Numbers between 1 and 500 that are divisible by 1000 = 0

Total Dollar amount earned by contractor is 55 only

2.Special Way of Numbering:

        As Contractor is clever he uses the special way of numbering the building(s) i.e., 001, 002,  .010,... 099, 100, ... 500
        If he follows the above pattern so he gains an extra amount is :

Total Numbers between 1 and 500 that are divisible by 10     = 50
Total Numbers between 1 and 500 that are divisible by 100   = 5
Total Numbers between 1 and 500 that are divisible by 1000 = 0
          Total Dollar amount earned by contractor is 55

Additional Zeroes for single digit numbers   2*9    = 18
Additional Zeroes for Double digit numbers 1*90 = 90

Total Dollar amount earned by contractor is 55 + 108 = 163



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Car on a wild stormy Night

Puzzle # 8

You are driving down the road in your car on a wild, stormy night, when you pass by a bus stop and you saw three people waiting for the bus:

1. An old lady who looks as if she is about to die.
2. An old friend who once saved your life.
3. The perfect partner you have been dreaming about.

Knowing that there can only be one passenger in your car, whom would you choose?


Solution
The old lady of course! After helping the old lady into the car, you can give your keys to your friend, and wait with your perfect partner for the bus.



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Merchant and his Gold Coin

Puzzle # 1
There is a Gold Shop and merchant has promised to give a Gold coin to any of his worker. But, merchant is so clever that he will give away the coin only if the worker fulfill his conditions 

1. Worker has to work in the shop for seven consecutive days.
2. On every day merchant has promised to give his share equally.
3. Merchant has decided to cut the Gold coin only twice in seven day(s)

Solution

Cut the Gold Coin in to three parts

First part has 4/7 of total Gold Coin

Second part has 2/7 of total Gold Coin

Third part  has 1/7 of total Gold Coin

First Day:

Merchant has to give 1/7 part of the Gold coin to servant

Second Day:

Merchant has to give 2/7 part of the Gold coin to servant and take back the 1/7 part of the Gold coin from servant

Third Day:

Merchant has to give 1/7 part of the Gold coin to servant, Now Servant has 1/7 & 2/7 part of coins with him.

Fourth Day:

Merchant has to give 4/7 part of the Gold coin to servant and take back the 1/7  and 2/7 part of the Gold coin from servant

Fifth Day:

Merchant has to give 1/7 part of the Gold coin to servant, Now Servant has 1/7 & 4/7 part of coins with him.

Sixth Day:

Merchant has to give 2/7 part of the Gold coin to servant and take back the 1/7 part of the Gold coin from servant. Now Servant has 2/7 & 4/7 part of coins with him.

Seventh Day:

Merchant has to give 1/7 part of the Gold coin to servant. Now Servant has 1/7, 2/7 & 4/7 part of coins with him.

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