# 10427 - Naughty Sleepy Boys

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Difficulty : medium

Solution Description :

Math problem

start 1 end 9:            1 digit number= 9             digit=1*9=9                      total digit=9
start 10 end 99:         2 digit number=90            digit=2*90=180                 total digit=9+180=189
start 100 end 999:     3 digit number=900          digit=3*900=2700              total digit=189+2700=2889
start 1000 end 9999: 4 digit number=9000         digit=4*9000=36000          total digit=2889+36000=38889
and so on............

You need to store start value and total digit for 1 digit number to 8 digit number
so you can got
start[0]=0                totaldigit[0]=0                block 0
start[1]=1                totaldigit[1]=9                block 1
start[2]=10              totaldigit[2]=189             block 2
start[3]=100            totaldigit[3]=2889           block 3
.................................................
start[8]=10000000   totaldigit[8]=788888889   block 8

Now input n
you can find easily n in which block.
if n=3 then it is in block 1 i.e. 1 digit number block,     because totaldigit[0]<n<totaldigit[1]
if n=10 then it is in block 2 i.e. 2 digit number block,    because totaldigit[1]<n<totaldigit[2]
if n=100 then it is in block 2 i.e. 2 digit number block,  because totaldigit[1]<n<totaldigit[2]

so, you can find the start number for this block
if n=10 then it is in block 2 and start number = start[block]=start[2]=10

now set m = n - totaldigit[block]     // if n=10 then m = 10 - totaldigit[2] = 10 - 9 = 1

now find the number (num) which contain n'th digit
set x =(long) m / block // if n=10 then x = 1/2 = 0, if n=11 then x = 2/2=1, if n=12 then x=3/2=1
if x*block == m then x = x-1
// for n=10 -> x=0, n=11 -> x=0, n=12 -> x=1
num = start[block]+x // for n=10 -> num=10+0=10, n=11 -> num=10+0, n=11 -> num=10+1=11
digitNum=m%block
if digitNum==0 then digitNum=block
// for n=10 -> digitNum=1, n=11 -> digitNum=2, n=12 -> digitNum=1

finally you got the ans
num             digitNum            ans
n=10         10                1                       1
n=11         10                2                       0
n=12         11                1                       1