Sum three, get one (Posted on 2007-04-25)

	Submitted by K Sengupta
Rating: 2.5000 (2 votes)
Solution:	(Hide)
If possible, let n < = a, b, c Then, a! + b! + c! > = 3n > n, a contradiction. Thus, n > a, b, c If in addition, n > 3, then: n! > 3 (n-1)! > = a! + b! + c!. This is a contradiction Accordingly, it follows that: n = 1, 2, or 3. A check for these values of n, yields: 3! = 2! + 2! + 2!. Hence n =3; a=b=c =2 is the only possible solution to the given problem.

	Subject	Author	Date
	Solution with explanation	FrankM	2020-04-09 11:47:30
	Solution	hoodat	2007-04-26 08:57:19
	Possible solution?	Mike C	2007-04-25 10:13:54
	One and only one	Old Original Oskar!	2007-04-25 10:06:05