License plates are issued systematically. In a state where the license plates contain three letters followed by three numbers, the following sequence of license plates could be issued: CMP998, CMP999, CMQ000, CMQ001, and so on. The most recent license plate issued in this state is AZY987, which has no repeated letters or digits. How many license plates must be issued after this one before a license plate will again have no repeated letters or digits?
Please show/explain each step!
Thanks!
2007-05-14 15:16:56 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Going in order:
AZY987 (starting point)
AZY988 (duplicate 8) - 1 plate
AZY989 (duplicate 9) - 1 plate
AZY99[0 to 9] (duplicate 9) - 10 plates
AZZ[000 to 999] (duplicate Z) - 1,000 plates
BAA[000 to 999] (duplicate A) - 1,000 plates
BAB[000 to 999] (duplicate B) - 1,000 plates
BAC00[0 to 9] (duplicate 0) - 10 plates
BAC010 (duplicate 0) - 1 plate
BAC011 (duplicate 1) - 1 plate
BAC012 - no duplicates
There will be 3,024 plates released with at least one duplicate letter or number, and the 3,025th plate will be BAC012 which has no repeated letters or digits.
2007-05-14 15:22:05 · answer #1 · answered by McFate 7 · 2⤊ 0⤋
azy987 + 3 = azy990
azy990 +10 = azz000
azz000 + 1000 = baa000
baa000 + 1000 = bab000
bab000 + 1000 = bac000
bac000 + 12 = bac012
3,025 plates
2007-05-14 15:23:08 · answer #2 · answered by vospire s 5 · 0⤊ 0⤋
I get 3024. Here's how.
AZY 988-999 will all have a repeated 8 or 9 = 12
AZZ xxx = 1000 [where xxx is 000 to 999]
BAA xxx = 1000
BAB xxx = 1000
BAC 000 to 011 = 12
So it will take 12+1000*3 + 12 = 3024. The first one will be BAC 012
2007-05-14 15:25:29 · answer #3 · answered by Kathleen K 7 · 0⤊ 0⤋
This sounds like a school problem, which means it's too difficult for me...
2007-05-14 15:20:19 · answer #4 · answered by Anonymous · 0⤊ 0⤋
complicated thing. check out into google and yahoo. just that can help!
2014-10-31 21:09:31 · answer #5 · answered by Anonymous · 0⤊ 0⤋
cheating on homework?
2007-05-14 15:19:42 · answer #6 · answered by michael45140 2 · 0⤊ 0⤋