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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