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Self-summing Numbers
A self-summing number starts with two arbitrary digits, after which each following digit is the sum of the previous two digits. For example: 78156112, because: 7+8=15; 1+5=6; 5+6=11; 1+1=2.
Note: This is not Fibonacci, because we are working with digits, not numbers. For this problem, we do: 78156112… . However, Fibonacci would be: 78152338… .
Challenger
Give the smallest self-summing number that contains 6 different digits.
Mastermind
A self-summing number is non-repeating when the same pair of digits does not occur more than once. For example: 31459 is non-repeating, however 3145914 is repeating.
How many non-repeating self-summing numbers exist in which all digits (0 through 9) appear at least once?