Quandaries
and Queries
What are the number of permutations (Combinations?) of a combination lock of a cylinder with four separate movable rings. Each ring has the numbers from one to six (six "permutations" per ring).
This is a bicycle lock.
I was told that it is 62 (6x6x6x6) = 1296.
Is this correct?.
Hi,
1296 is correct.
Each ring has 6 possible positions. Select a number on the first ring. You can do this in 6 possible ways. Now, for each of the 6 possible choices for the first ring, you have 6 possibilities for the second. Thus for the first two rings there are 6 
6 = 36 possibilities.
In a similar way, for each of the 36 possible choices for the first two rings there are 6 possibilities for the third and thus 63 possibilities for the first tree rings, and 64 for all four.
Penny
