Friday, September 26, 2014

JMO, numbers

In the number 259260261262263....490491492. How many 8's are there?



Answer:

kindly note the number carefully.
All numbers between 259 to 492 are written side by side.

now, between any hundred consecutive natural numbers, the number of any digit (1,2,....9) in units place is 10 and the number of any digits (1,2,...9) in 10's place is also 10.

Now, between 458 and 259 there are ( 458 - 259 + 1 = 200 numbers)

Since there are 200 numbers, the number of 8's in the units place is 2 x 10 = 20
and the number of 8's in the ten's place is also 2 x 10 = 20

between 492 and 459 we have in 10's place, (489 - 480 + 1 = 10 numbers)
in the units place we have 468, 478, 488 ---- i.e. 3 nos.

So, total number of 8's in the big number = 20 + 20 + 10 + 3 = 53

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