Combinatorics | Number Theory Answers

My question is write the number that is one hundred million more than 15,146,481

Let 1210AB be a six-digit number with two digits (A and B) being unknown. Assume that the number shown is a multiple of both 9 and 11. Use the divisibility test for 9 to find the least positive residue of A + B (mod 9). Similarly, use the divisibility test for 11 to find the least positive residue of A – B (mod 11). Use these results to find the values of A and B that will make 1210AB a multiple of 99. Hint: A + B must be between 0 and 18, and A – B must be between –9 and 9.

What is the sense of the equations: ABC = A; A ∪ B ∪ C = A?

Is it possible to set 10 bus routes in the city and set the stations on them so that if we take any 8 of them there always will be a station not belonging to any of them, but any 9 routes pass through all the stations?

Is it possible to divide 2n persons into pairs in 2n-1 different ways so that each person was paired with each other exactly in the same division?