Question 61

ABC is a three-digit number in which A > 0. The value of ABC is equal to the sum of the factorials of its three digits. What is the value of B?

Solution

The values of 1!, 2!, 3!, 4!, 5!, 6! and 7! are 1, 2, 6, 24, 120, 720 and 5040 respectively.

So, the digits must lie from 1 to 6 only to satisfy the conditions.

6 cannot be one of the digits as the at least one digit in the final number is more than 6.

145 = 1! + 4! + 5!

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