



 
Hi Aeriel, Suppose the lock had only 1 tumbler then, since it has 5 possible heights, 5 different keys are possible. Now suppose you add a tumbler then regardless of the height you have set for the first tumbler you have 5 choices for the height of the second tumbler. Hence for a 2 tumbler lock there are $5 \times 5 = 5^2$ different possible keys. Now suppose you add a third tumbler. Again regardless of the height you have set for the first two tumblers you have 5 choices for the height of the third tumbler. Hence for a 3 tumbler lock there are $5^2 \times 5 = 5^3$ different possible keys. Continue,  


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