The puzzle is here.
Gist: Are there two 7 digits numbers, each comprising of the digits 1,2,3,4,5,6,7 such that one divides the other?
Solution
Each number must leave a remainder 1 when divided by 9, as the sum of digits is 1 + 2 + ... + 7 = 1 modulo 9.
Now the larger number cannot be more than seven times the smaller number (largest possible digit is 7 and both are seven digit numbers).
Thus if the smaller leave a remainder 1, then the larger cannot.
Thus there aren't such two numbers.
Gist: Are there two 7 digits numbers, each comprising of the digits 1,2,3,4,5,6,7 such that one divides the other?
Solution
Each number must leave a remainder 1 when divided by 9, as the sum of digits is 1 + 2 + ... + 7 = 1 modulo 9.
Now the larger number cannot be more than seven times the smaller number (largest possible digit is 7 and both are seven digit numbers).
Thus if the smaller leave a remainder 1, then the larger cannot.
Thus there aren't such two numbers.
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