Quiker way needed

[ajprasad]

How many times is the digit 5 written if number from 1 to 1000 are written?

Answer is 300. Is there a quick way of solving this?

[Ankost]

When 5 is the hundredth digit, the number 5** can have different numbers as tenth digit 10 times and as a unit digit also 10 times. 1*10*10*3=300. Multiplied by 3 because we need to consider cases when 10*1*10 and 10*10*1, when 5 is the tenth digit and the unit digit.

[phishman2112]

We have to consider only 2 special cases:
1.)from 0 to 100, # of 5s = 20; same for 101 to 200 etc all the way to 900 to 10000. Therefore total 5s = 20x10=200.
2.) 500 to 599=100 5s (in addition to 20 from the tenths and units place)

Total=300

[RamN]

Breaking into Units, Tens and Hundreds wil make the thing easier.

Taking by 1 set at once = 5 in Units = 10 times in 100 = 10 * 100
Likewise calculate 5 in Tens = 100
Likewise calculate 5 in hundres = 100

Sum = 300

[arason]

Originally Posted by RamN

Breaking into Units, Tens and Hundreds wil make the thing easier.

Taking by 1 set at once = 5 in Units = 10 times in 100 = 10 * 100
Likewise calculate 5 in Tens = 100
Likewise calculate 5 in hundres = 100

Sum = 300

Nice method. Thanks for the post.