Ivan and Adeline are in a classroom with a chalkboard. They are standing on different halves of the board, and on each half, the number \(2\) is written. When Ivan’s teacher gives a signal, Ivan multiplies the number on his side of the board by \(-2\) and writes the answer on the board, erasing the number he started with. Adeline does the same on each signal, except that she multiplies by \(2\). The teacher gives \(10\) signals in total. How many times (including the initial number) do Ivan and Adeline have the same number written on the board?
伊万和艾德琳在一间有黑板的教室里。两人分别站在黑板的两半区域，每一半区域上都写着数字 \(2\)。老师发出一次指令时，伊万将自己那一侧黑板上的数字乘以\(-2\)，擦掉原来的数字，写下计算结果。艾德琳在每次收到指令时做类似操作，只不过她乘以\(2\)。老师一共发出 \(10\) 次指令。算上初始数字在内，伊万和艾德琳黑板上的数字相同的情况一共出现多少次？