goyalsau wrote:If x represents the sum of all the positive three-digit numbers that can be constructed using each of the distinct nonzero digits a, b, and c exactly once, what is the largest integer by which x must be divisible?
11
22
222
3
6
The solutions offered above that arrived at the correct answer (222) are perfect, but for those who worry that they wouldn't be able to think that way during the test, another approach would be to plug in a few times.
123+132+213+231+321+312 = 1332. 1332/222=6.
235+253+325+352+523+532 = 2220. 2220/222=10.
147+174+417+471+714+741 = 2664. 2664/222=12.
By now we could feel pretty secure that 222 is the largest factor that will work.
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