For some 99-digit number k, there exist two different 100-digit numbers n such that the sum of all natural numbers from 1 to n ends in the same 100 digits as the number kn, but is not equal to it. Prove that k-3 is divisible by 5.
You are handed a following list and asked to select one and to explain your choice:
White, red, pink, green, apple, peach, orange, lemon, kiwi, purple, asparagus, grape.
What, in your opinion, are the interviewers’ expectations?