12.4.14 Various Olympiad problems

Problem: Several not necessarily different natural numbers are written on the board in one line from left to right. It is known that each next number, except for the first one, is either greater than the previous one by 1 , or two times smaller than the previous one. a) It is possible that the first number is 12 , and the seventh one is 2 ? b) It is possible that the first number is equal to 1200 , and the \( 25^{\text {th }} \) one is equal to 63 ? c) What is the smallest amount of numbers that can be written on the blackboard if the first number is 1200 and the last number is 5 ?