The famous Kohinoor diamond has been put on display in a certain museum. The museum authorities have installed an electronic lock which has N buttons, each with a different symbol. To open the lock one must select the correct combination of the symbols, irrespective of the order in which the buttons are pressed. When each button is pressed it lights up. If the correct combination is lit, the lock immediately opens. On the side of the lock is a reset button which will turn off all the lights.
The Jewel Thief visited the museum and noted down all the symbols. That night, he returned to steal the precious gem. Due to shortage of time, he must open the lock as fast as possible.
What is the minimum number of presses needed to guarantee that the lock will open (including both symbols and reset)? Assume that all the lights are off when he arrives.
Let 1, 2, ..., N be the buttons and 0 be reset. Here are the first few solutions.
N=1: 1
1
N=2: 4
1202
N=3: 9
123023031
N=4: 22
1234023403410412013024
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Posted by Math Man
on 2019-04-21 21:44:34 |
Answers for small N
