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1 digit #s= 9 --> # plates used for 1 digit #s= 9 * 1 (digit) = 9 2 digit #x= 9 * 10 =90 --> # plates used for 2 digit #s= 9 * 10 * 2 = 180 there are 9 available digits for the tens slot, and 10 (0-9) for the ones slot. *2 because this number will be using 2 plates (2 digits)

total so far = 189

2121-189=1023 which is the number of plates left we have to work with for the 3 digit numbers.

1023/3= # of 3 digit numbers we can create from these plates = 341

Don't treat this as a P And C question. The best way to go on about this is to imagine urself as a plate manufacture who has a constraint of manufacturing only 1212 plates, you can imprint whatever number you want on the plate but limited to 1212 plates. Also one more constraint is every plate should have a single digit on it. Now imagine u have been given an order to print those numbers with a series of consecutive number in mind. So you print 1,2,3,4 till 9 then you remember you cant print a 10 on a single tile but you can print 1 and 0 on different tiles hence you will use 2 tiles for 1 house after number 9(bummer and waste of tile but can't help it) so till 99 house number u have used 9 + 90x2 tiles i.e 189 tiles. Ok you had 1212 tiles but now you have used up 189. So you will be left with 1023 tiles. How many 3 digits houses can you make of these 1023 tiles. 341. Now add 1 digit tiles used for 1 digit consecutive number. 1 digit tiles used for 2 digits consecutive number and 1 digit tiles used for 3 digits consecutive number.