Question 88
299 zeros and one one are written in a circle. The following moves are allowed:
* You can select all numbers simultaneously and subtract both of its neighbouring numbers from each number.
* You can select two numbers such that there are exactly two numbers between them, and either increase both selected numbers by 1 or decrease both of them by 1.
Can we obtain through a finite number of moves that the following numbers are written in a circle:
a) two consecutive ones and 298 zeros?
b) three consecutive ones and 297 zeros?
* You can select all numbers simultaneously and subtract both of its neighbouring numbers from each number.
* You can select two numbers such that there are exactly two numbers between them, and either increase both selected numbers by 1 or decrease both of them by 1.
Can we obtain through a finite number of moves that the following numbers are written in a circle:
a) two consecutive ones and 298 zeros?
b) three consecutive ones and 297 zeros?