Digital Factorial!

Number Theory Level 3

Find a 3-digit integer which is can be expressed as the sum of factorial of its digits.

A B C ‾ = A ! + B ! + C ! \overline{ABC} = A! + B! + C!


Notation: ! ! is the factorial notation. For example, 8 ! = 1 × 2 × 3 × ⋯ × 8 8! = 1\times2\times3\times\cdots\times8 .


The answer is 145.

Adarsh Shetty by Adarsh Shetty , 27, India

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2 solutions

Rimba Erlangga
Jan 23, 2015

You can see that a , b , c ≤ 6 a,b,c \leq 6 , then you can brute force

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Bill Bell
Jan 23, 2015

That number is not unique. Looking up to n=1,999,999 I found another, 40585.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you @Bill Bell for helping me out...

Adarsh Shetty - 6 years, 4 months ago

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My pleasure! Interesting question.

Bill Bell - 6 years, 4 months ago

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