in how many ways can you represent the number 123456789 using only 1's and 2's

eg: 7 can be represented in 4 ways as:
1+1+1+1+1+1+1
2+1+1+1+1+1
2+2+1+1+1
2+2+2+1

Question

in how many ways can you represent the number 123456789 using only 1's and 2's

eg: 7 can be represented in 4 ways as:
   1+1+1+1+1+1+1
   2+1+1+1+1+1
   2+2+1+1+1
   2+2+2+1

anonymous · Answer

Conceptually, I recommend thinking about the two extreme cases: All 1s added together, and all 2s added together. All other ways are combinations of these two.

anonymous · Answer

Its answer is 61728395 it dont know it come

anonymous · Answer

Well in the extreme case you know that 123456789 = 2x + 1 where x is the maximum number of 2's you can have and still be less than 123456789

anonymous · Answer

so solve that for x.

anonymous · Answer

If you quickly run through 1-10, you may see a pattern forming also.

anonymous · Answer

great polpak

anonymous · Answer

Well looking at what you listed there you can see that you have the sum of some number of 2's and some number of 1's. You know that you cannot have all 2's since it's an odd number. So on the extreme end you'll have a whole lot of 2's and one 1.