Find out at least five cities in India or any other places in the World where ‘Odd-Even’ rule was implemented?a)What was the fine policy in any of the two cities where ‘odd-even’ policy was imposed? How much was the amount of fine charged from the defaulters, in these two cities?b)Calculate the total fine collected by each of the cities. Show the working/calculation.c)Name the city in which the fine collection was highest?Odd Rules, Even Conquers!!i)Did you know that the difference between the squares of two consecutive numbers is always odd? Verify it with three consecutive 3-digit numbers.ii)More interestingly, Did you know that these differences would form the odd number series when all the whole numbers are involved? Well!! Find out yourself! Use the above numbers and observe whether any series is being formed.iii)There are rules that tell us what happens when you add, subtract, or multiply even and odd numbers. In any of these operations, you will always get a particular kind of whole number. Find out the rules. What happens when we divide? Do we get odd or even number? Or we get something else? Take specific numbers and work it out.
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In India in the recent years, the odd even rule was implemented to ease the traffic based on license plate numbers. Long ago some such a rule was implemented in Paris, Mexico city, a city in China too. That was also to ease the traffic on the routes.
The amount of fine for violating the odd-even license plate rule is Rs 2,000.
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(i) difference between successive squares.
(n+1)² - n² = [n+1-n] * [n+1+n] = 2 n + 1
Clearly it has to be an odd number.
101² - 100² = 201
102² - 101² = 203
103² - 102² = 205
These differences form an arithmetic series with a common difference of 2.
These numbers form a sequence of consecutive odd numbers.
odd number * odd number = odd number
odd number * even number = even number
odd / odd number = odd number
odd / even number = fraction
even / odd number = fraction or even number
odd + odd = even
odd - even = odd
even - even = even
even + even = even
The amount of fine for violating the odd-even license plate rule is Rs 2,000.
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(i) difference between successive squares.
(n+1)² - n² = [n+1-n] * [n+1+n] = 2 n + 1
Clearly it has to be an odd number.
101² - 100² = 201
102² - 101² = 203
103² - 102² = 205
These differences form an arithmetic series with a common difference of 2.
These numbers form a sequence of consecutive odd numbers.
odd number * odd number = odd number
odd number * even number = even number
odd / odd number = odd number
odd / even number = fraction
even / odd number = fraction or even number
odd + odd = even
odd - even = odd
even - even = even
even + even = even
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