Latest self Aptitude Question SOLUTION: Find a 5-digit integer whose value is equal to the sum of the factorials of its own digits.

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(#M40010082) SELF question Keep an EYE

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

jyotish r (11 years ago)

Solved chaitanya Read Solution (1)

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chaitanya  (11 years ago)

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

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