Math CentralQuandaries & Queries


Question from Tom, a student:

I need to open a lock box from my parent's estate. The combination is a simple 4 number lock. The last two numbers are 33. Numbers can be used more than once.What are the possible combinations?


Hi Tom,

If the last two digits are 33 then you only need tofind the first two. There are 10 possibilities for the first digit and 10 for the second and hence there are $10 \times 10 = 100$ possibilities for the first two digits. You can even list them. They are $00, 01, 02, \cdot \cdot \cdot 09, 10,11, \cdot \cdot \cdot, 19, 20, 21, \cdot \cdot \cdot, 98, 99$


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