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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

Harry Houdini selected three non-zero digits a, b, c and then formed a number and all its cyclical permutations with them. The average of all the numbers he formed was divisible by:

(Harry Houdini was a Hungarian-born American, one of the most famous magicians in history.)

The numbers can be:

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and their sum has the property that it is a multiple of 111:

equation

equation

The average is:

equation

and it is always divisible by 37.