Question 37521: Paul's calculator can make only 2 operations; add 12 to the number displayed, or subtract 7 from it.Today, it shows the number 1998. what is the minimal number of steps needed to display the number 2000?
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Since you need to increase the display by only two, you need to find a multiple of positive twelve and a multiple of negative seven that have a difference of positive two...
The brute force way is to just list those multiples:
12, 24, 36, 48, 60, 72, 84, 96, ...
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, ...
until you find a pair differing by exactly two...
Though 12 and 14 differ by two, that would be negative two and incorrect...
The correct pair is 72 and 70, and the number of keystrokes to get there would be
6 + 10 = 16 keystrokes
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