Find a 5-digit integer whose value is equal to the sum of the factorials of its own digits.

• factorial values from 0 to 9
  0!=1
  1!=1
  2!=2
  3!=6
  4!=24
  5!=120
  6!=720
  7!=5040
  8!=40320
  9!=362880 now given that it is a 5 digit number
  
  so we can eliminate 9! from the count.
  but
  
  0-9 numbers can be arranged in 5 digit numbers in 9x9x9x9x9=59049(if repetition)
  If not:
  9x8x7x6x5=15120
  
  by crosscheck we can eliminate numbers with 1,2,3,6,7,8,9 numbers in twice or thrice or more
  
  40585
  4!+0!+5!+8!+5!= 24 + 1 + 120 + 40320 + 120
  = 40585
• 12 years agoHelpfull: Yes(1) No(3)