How masses ways can you trade name a dollar in need using pennies?
Answers:
Um, if you scrounging next to tweaking (quarters, dimes, nickels), I counted 29. If you include a 1/2 dollar coin, I found 40. If I include a dollar coin, it's 41.
20 n , 1 d + 18 n , 2 d + 16 n , 3 d + 14 n , 4 d + 12 n , 5 d + 10 n , 6 d + 8 n , 7 d + 6 n , 8 d + 4 n , 9 d + 2 n , 10 d , 1 q + 15 n , 1 q + 1 d + 13 n , 1 q + 2 d + 11 n , 1 q + 3 d + 9 n , 1 q + 4 d + 7 n , 1 q + 5 d + 5 n , 1 q + 6 d + 3 n , 1 q + 7 d + 1 n , 2 q + 10 n , 2 q + 1 d + 8 n , 2 q + 2 d + 6 n , 2 q + 3 d + 4 n , 2 q + 4 d + 2 n , 2 q + 5 d , 2 q + 5 n , 3 q + 1 d + 3 n , 3 q + 2 d + 1 n ;
near the 1/2 make a payment:
4 q , 1 h + 10 n , 1 h + 1 d + 8 n , 1 h + 2 d + 6 n , 1 h + 3 d + 4 n , 1 h + 4 d + 2 n , 1 h + 5 d , 1 h + 1 q + 5 n , 1 h + 1 q + 1 d + 3 n , 1 h + 1 q + 2 d + 1 n , 1 h + 2 q , 2 h;
next to the $1 coin give:
1 D.
I could be wrong.
I did it the unyielding style, I needed some excercise.
The number of ways of adapt for a dollar is the coefficient of x^100 within the expansion of (1/(1 - x))(1/(1 - x^5))(1/(1 - x^10))(1/(1 - x^25))(1/(1 - x^50)).
If you didn't tight adapt, very well, in that's simply too heaps ways to enumerate!
23
I guess I miscounted