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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

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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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