密碼鎖
一個有3 個旋鈕,每個位置的號碼數分別是a、b、c 的密碼鎖,如果有兩個位置的數字正確就能打開,最少需要猜多少次才能保證打開這個鎖。在本論文中,我們將密碼鎖三個位置的號碼數分成:a=b=c=n、a=b<c,a=b>c 和a>b>c 四個部份來討論。前兩部份的研究已經找到最少次數開鎖的方法 ,後兩部份則是給了一個演算法可求出開鎖次數的上界。If a combination lock with three rotate wheels can be opened when two wheels are adjusted to the correct numbers, then how many guesses does one need to make before he or she can actually open this lock? Let us say a , b and c respectively represents the numbers that should show on each wheel. In this paper, we divide the numbers into shown on the three wheels, and they are a = b = c = n , a = b c and a = b < c . The research on the first two combinations has already given us the method we can use to open he lock with the least number of trials. On the other hand, the latter two offer us an algorithm that can be uses to obtain the upper bound of tries needed to open the lock.