Can you find a number such that if we multiply that number by 1 or 2 or 3 or 4 or 5 or 6, then the resultant number contains same all digits (of course in a different place)
142857
1×142857=142857 2×142857=285714 3×142857=428571 4×142857=571428 5×142857=714285 6×142857=857142
My house number is such that, when divided by 2, 3, 4, 5 or 6 it will always leave a remainder of 1.
However, when divided by 11 there is no remainder. What is my house number?
Calculate the number of ordered triples (A1, A2, A3) such that:
A1 ∪ A2 ∪ A3 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A1 ∩ A2 ∩ A3 = ∅
Write your answer as 2a3b5c7d where a, b, c, d are non-negative integers.
