A 10 digit positive number is said to be a
“LearnHub”number if its digits are all
distinct and it is a multiple of 11111. How
many “LearnHub” numbers are there?

• 10 digit number and all digits distinct
  Sum of digits = 45
  Number is divisible by 9
  
  Number is divisible by 99999
  If number is of form abcdefghij, then
  
  abcde + fghij = 99999
  a + f = b + g = c + h = d + i = e + j = 9
  We have 5 such pairs (0, 9), (1, 8 ), (2, 7), (3, 6), (4, 5)
  
  So, we can choose abcde in 9*8*6*4*2 = 3456 ways as leading zero is not permitted.
  a can have value from 1 to 9 and corresponding value of f is also fixed.
  b can have value from balance 8 values ( leaving values fixed for a and f from 0 to 9) and corresponding value of g is also fixed.
  ..
  ..
  Once abcde is chosen, fghij is automatically chosen
  
  So, 3456 such numbers
• 12 years agoHelpfull: Yes(1) No(0)