An algebra problem by Sai Teja Prasanth
Algebra
Level
pending
The number of natural numbers which are smaller than 2x10^8 and which can be written by means of the digits 1 and 2.
586
868
768
766
824
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1 solution
The required numbers are 1,2,11,12,21,22,........1222222222. Let us calculate hoe many numbers these are.The are two one digit numbers .there are 2^2 two digit numbers 2^3 three digit numbers and so on.There are 2^8 two digit such numbers.All the nine digit numbers beginning with 1 and written by means of 1 and 2 are smaller than 2 x 10^8 Thus there are 2^8 such nine digit numbers
Hence the required number of numbers is 2+4+8+16+32+..............2^8+2^8. =2(2^8-1)/(2-1)+2^8=2^9-2+2^8=766