SOLUTION: There is a box with a padlock You can open the box if you will be able to know the 4-digit code in the padlock. If the first digit of the 4-digit code is 5, how many possible codes
Question 1193059: There is a box with a padlock You can open the box if you will be able to know the 4-digit code in the padlock. If the first digit of the 4-digit code is 5, how many possible codes are there if the repetition of the digit code is allowed?
Found 2 solutions by Theo, ikleyn:Answer by Theo(13342) (Show Source): You can put this solution on YOUR website! there is one possible digit for the first position and 9 possible digits each for the next 3 digits.
the number of possible combinations is 1 * 9 * 9 * 9 = 9^3 = 729.
to understand how this works, assume there are only 2 possible digits for the next 3 positions.
the number of possible combinations would then be 1 * 2 * 2 * 2 = 2^3 = 8.
assuming the 2 possible numbers for each position were 2 and 3, then you would get:
5222
5223
5232
5233
5322
5323
5332
5333
the same concept applies when there are 9 possible numbers for each digit, except the number of combinations are too numerous to individually display.
Of 4 possible digit positions, the first position is just occupied by the digit of 5.
Three other positions are free, and we can put any of 10 possible digits from 0 to 9 in any of these 3 positions.
It gives = 1000 possible digit codes. ANSWER
Solved (correctly).
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Ignore answer by @Theo, since it is INCORRECT.
I don't know why @Theo decided about 9 digits.
Working base 10, we always have 10 possible digits.