Number 3 can be expressed by using 1 and 2 in 3 distinct ways I,e, 1+1+1, 1+2, 2+1; number 4 in 5 ways: 1+1+1+1 , 2+1+1, 1+2+1, 1+1+2, and 2+2.
Using the digits 1 and 2 as summands, in how many ways may be 26 expressed?
Bonus: Generalize the process for number N.
F(N) is the Nth Fibonacci number. 0,1,1,2,3,5,...
The 3rd Fibonacci number is 2 and the 4th is 3 so there is an offset of +1.
F(N)=F(N-1)+F(N-2) because you can take every F(N-1) way and add +1 at the end and take every F(N-2) way and add +2 at the end.
The number 26 can be expressed in F(27)=196418 ways
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Posted by Jer
on 2023-05-05 11:24:11 |
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